Inclusion Criteria:

          -  Patients must be 18 years of age or older.

          -  Patients with the following histologically confirmed diagnoses will be eligible for
             enrolment: p16 positive SCCHN; squamous cell carcinoma of the cervix; p16 positive
             squamous cell carcinoma of the vagina or vulva; p16 positive squamous cell carcinoma
             of the penis; p16 positive squamous cell carcinoma of the anus or anal canal; EBER
             positive NPC; EBER positive Hodgkins and non-hodgkins lymphoma.

          -  Note: patients with p16 positive SCC of unknown primary origin meeting the minimum
             life expectancy and performance status requirements will also be eligible for
             enrollment, as the majority of these patients may be assumed to represent
             HPV-associated disease.

          -  Patients must be capable of providing consent to enrolment and treatment.

          -  Patients with a performance status of ECOG 0-1(51) will be eligible for enrolment (see
             appendix 1).

          -  Measurable disease must be present according to irRECIST criteria(50).

          -  Women of child bearing potential (WOCBP) must have a negative serum (or urine)
             pregnancy test at the time of screening.

          -  Patients of childbearing / reproductive potential should use highly effective birth
             control methods, as defined by the investigator, during the study treatment period and
             for a period of 60 days after the last dose of study drug. A highly effective method
             of birth control is defined as those that result in low failure rate (i.e. less than
             1% per year) when used consistently and correctly.

          -  Note: abstinence is acceptable if this is established and preferred contraception for
             the patient and is accepted as a local standard.

          -  Female patients who are breast-feeding should discontinue nursing prior to the first
             dose of study treatment and until 120 days after the last dose of study drug.

          -  Absence of any condition hampering compliance with the study protocol and follow- up
             schedule; those conditions should be discussed with the patient before registration in
             the trial.

          -  The following adequate organ function laboratory values must be met:

          -  Hematological:

               -  Absolute neutrophil count (ANC) >1.5 x109/L

               -  Platelet count >100 x109/L

               -  Hemoglobin >9 g/dL (may have been transfused)

          -  Renal:

             o Estimated creatinine clearance ≥ 30 mL/min according to the Cockcroft-Gault formula
             (or local institutional standard method)

          -  Hepatic:

               -  Total serum bilirubin <1.5x ULN

               -  AST and ALT <2.5x ULN (or ≤ 5 x ULN for subjects with documented metastatic
                  disease to the liver)

               -  Serum albumin > 25 g/L

          -  Coagulation:

               -  International Normalized Ratio (INR) <1.5x ULN (unless patient is receiving
                  anticoagulant therapy as long as PT or PTT is within therapeutic range of
                  intended use of anticoagulants)

               -  Activated Partial Thromboplastin Time (aPTT) <1.5x ULN (unless patient is
                  receiving anticoagulant therapy as long as PT or PTT is within therapeutic range
                  of intended use of anticoagulants)

        Exclusion Criteria:

          -  History of pneumonitis requiring treatment with steroids.

          -  History of interstitial lung disease.

          -  Clinically significant (i.e., active) cardiovascular disease: cerebral vascular
             accident/stroke (< 6 months prior to enrollment), myocardial infarction (< 6 months
             prior to enrollment), unstable angina, congestive heart failure (≥ New York Heart
             Association Classification Class II), or serious cardiac arrhythmia requiring
             medication.

          -  History of another malignancy or a concurrent malignancy;

          -  Exceptions include patients who have been disease-free for 5 years, or patients with a
             history of completely resected non-melanoma skin cancer or successfully treated in
             situ carcinoma are eligible, for example cervical cancer in situ.

          -  Active brain metastases or leptomeningeal disease.

          -  Patients with treated brain metastases that are stable for 6 weeks will be eligible
             for enrolment.

          -  Diagnosis of immunodeficiency.

          -  Current use of immunosuppressive medication, EXCEPT for the following: a. intranasal,
             inhaled, topical steroids, or local steroid injection (e.g., intra-articular
             injection); b. Systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone
             or equivalent; c. Steroids as premedication for hypersensitivity reactions (e.g., CT
             scan premedication).

          -  Prior organ transplantation including allogenic stem-cell transplantation.

          -  Known history of human immunodeficiency virus (HIV).

          -  Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive
             HBV surface antigen or HCV RNA if anti-HCV antibody screening test positive).

          -  Active autoimmune disease that might deteriorate when receiving an immuno-stimulatory
             agent. Patients with diabetes type I, vitiligo, psoriasis, or hypo- or hyperthyroid
             diseases not requiring immunosuppressive treatment are eligible.

          -  Patients with hyperthyroidism or hypothyroidism but that are stable on hormone
             replacement will not be excluded.

          -  Active infection requiring systemic therapy.

          -  Vaccination within 4 weeks of the first dose of Avelumab and while on trials is
             prohibited except for administration of inactivated vaccines.

          -  Patient will not be eligible if the patient is or has an immediate family member
             (e.g., spouse, parent/legal guardian, sibling or child) who is investigational site or
             sponsor staff directly involved with this trial, unless prospective IRB approval (by
             chair or designee) is given allowing exception to this criterion for a specific
             subject.

          -  Persisting toxicity related to prior therapy (NCI CTCAE v. 4.03 Grade > 1); however,
             alopecia, sensory neuropathy Grade ≤ 2, or other Grade ≤ 2 not constituting a safety
             risk based on investigator's judgment are acceptable.

          -  Known prior severe hypersensitivity to investigational product or any component in its
             formulations, including known severe hypersensitivity reactions to monoclonal
             antibodies (NCI CTCAE v4.03 Grade ≥ 3).

          -  Other severe acute or chronic medical conditions including immune colitis,
             inflammatory bowel disease, immune pneumonitis, pulmonary fibrosis or psychiatric
             conditions including recent (within the past year) or active suicidal ideation or
             behavior; or laboratory abnormalities that may increase the risk associated with study
             participation or study treatment administration or may interfere with the
             interpretation of study results and, in the judgment of the investigator, would make
             the patient inappropriate for entry into this study.