A preparation of allogeneic, off-the-shelf (OTS), T-lymphocytes, derived from healthy donors, that have been genetically modified using a proprietary synthetic endonuclease-based system to express a chimeric antigen receptor (CAR) targeting the tumor-associated antigen (TAA) CD20 (cluster of differentiation 20), with potential immunostimulating and antineoplastic activities. Upon administration, allogeneic anti-CD20-CAR T-cells PBCAR20A specifically recognize and kill CD20-expressing tumor cells. The CD20 antigen, a non-glycosylated cell surface phosphoprotein, is a B-cell specific cell surface antigen expressed in B-cell lineage malignancies.