Inclusion Criteria:

          -  Signed written informed consent obtained prior to study procedures

          -  Histologically-confirmed relapsed or refractory CD20+ B-cell lymphoma of one of the
             following types, with documented disease progression or recurrence following the
             immediate prior therapy:

               -  DLBCL, regardless of cell of origin or underlying molecular genetics

               -  MCL

               -  PMBCL

               -  Gr3b-FL

               -  TH-FL

          -  Biopsy-confirmed CD20+ expression of the underlying malignancy by immunohistochemical
             staining or flow cytometry between the most recent dose of an anti-CD20 monoclonal
             antibody (mAb) and study enrollment

          -  At least 1 measurable lesion on imaging. Lesions that have been previously irradiated
             will be considered measurable only if progression has been documented following
             completion of radiation therapy

          -  Must have received adequate prior therapy for the underlying CD20+ B-cell lymphoma,
             defined as an anti-CD20 mAb in combination with an anthracycline-containing
             chemotherapy regimen (i.e. chemo-immunotherapy) and at least one of the following:

               -  biopsy-proven refractory disease after frontline chemo-immunotherapy

               -  relapse within 1 year from frontline chemo-immunotherapy and ineligible for
                  autologous hematopoietic stem cell transplant (auto-HSCT)

               -  For subjects with DLBCL, PMBCL, and Gr3b-FL: relapsed or refractory disease
                  following at least 2 prior regimens or following an auto-HSCT

               -  For subjects with TH-FL: relapsed or refractory disease following at least 2
                  prior regimens or following an auto-HSCT. At least 1 prior regimen with an
                  anti-CD20 mAb in combination with chemotherapy is required following documented
                  transformation

               -  For subjects with MCL (confirmed with cyclin D1 expression or evidence of
                  t(11;14) by cytogenetics, fluorescent in situ hybridization (FISH) or PCR):
                  relapsed or refractory disease after at least 1 prior regimen with
                  chemo-immunotherapy (prior auto-HSCT is allowable)

          -  Karnofsky performance scale ≥ 60%

          -  Life expectancy of at least 6 months

          -  ANC > 1000/µL

          -  Platelet count > 50,000/µL

          -  For women of childbearing potential (defined as physiologically capable of becoming
             pregnant), agreement to use of highly effective contraception for at least 1 year
             following ACTR087 infusion. For men with partners of childbearing potential, agreement
             to use effective barrier contraception for at least 1 year following ACTR087 infusion

        Exclusion Criteria:

          -  Known active central nervous system (CNS) involvement by malignancy. Subjects with
             prior CNS involvement with their lymphoma must have completed effective treatment of
             their CNS disease at least 3 months prior to enrollment with no evidence of disease
             clinically and at least stable findings on relevant CNS imaging

          -  Prior treatment as follows:

               -  alemtuzumab within 6 months of enrollment

               -  fludarabine, cladribine, or clofarabine within 3 months of enrollment

               -  external beam radiation within 2 weeks of enrollment

               -  mAb (including rituximab) within 2 weeks of enrollment

               -  other lymphotoxic chemotherapy (including steroids except as below) within 2
                  weeks of enrollment

               -  experimental agents within 3 half-lives prior to enrollment, unless progression
                  is documented on therapy

          -  Serum creatinine ≥ 1.5 X age-adjusted upper limits of normal (ULN)

          -  Pulse oximetry < 92% on room air

          -  Direct bilirubin ≥ 3.0 mg/dL (50 mmol/L)

          -  Alanine transaminase (ALT) ≥ 3 times the ULN, unless determined to be directly due to
             lymphoma.

          -  Aspartate transaminase (AST) ≥ 3 times the ULN, unless determined to be directly due
             to lymphoma

          -  Class III or IV heart failure as defined by the New York Heart Association (NYHA),
             history of cardiac angioplasty or stenting, documented myocardial infarction or
             unstable angina within 6 months prior to enrollment, cardiac ejection fraction of <
             45%, or other clinically significant cardiac disease

          -  Clinical history of, prior diagnosis of, or overt evidence of autoimmune disease,
             regardless of severity

          -  Clinically significant active infection, in the judgment of the investigator

          -  Pregnancy (negative serum pregnancy test to be obtained within 6 days prior to
             enrollment for subjects of childbearing potential)

          -  Breastfeeding

          -  Primary immunodeficiency

          -  Seropositive for Human Immunodeficiency Virus (HIV) 1 or HIV 2, or positive hepatitis
             B surface antigen (HBsAg) or hepatitis C antibody

          -  Will need or has needed active treatment of a second malignancy within the prior 3
             years before enrollment, other than FL, non-melanoma skin cancers, localized prostate
             cancer treated with curative intent, or cervical carcinoma in situ

          -  Is unable to receive any of the agents used in this study due a history of severe
             immediate hypersensitivity reaction (e.g. hypersensitivity to dimethyl sulfoxide
             (DMSO))

          -  History of prior allogeneic HSCT

          -  History of Richter's transformation from CLL

          -  Prior infusion of a genetically modified therapy