A preparation of a subset of allogeneic T-lymphocytes that express only gamma chain and delta chain T-cell receptors (TCRs) and that are engineered to express a chimeric antigen receptor (CAR) targeting the tumor-associated antigen (TAA) CD20 (cluster of differentiation 20), with potential immunomodulating and antineoplastic activities. Upon administration, allogeneic CD20 CAR-grafted gamma delta T-cells ADI-001 specifically target and bind to tumor cells expressing CD20. This induces secretion of pro-inflammatory cytokines and results in the lysis of CD20-expressing tumor cells. Gamma delta T-lymphocytes play a key role in the activation of the immune system and do not require major histocompatibility complex (MHC)-mediated antigen presentation to exert their cytotoxic effect. The CD20 antigen, a non-glycosylated cell surface phosphoprotein, is a B-cell specific cell surface antigen overexpressed in B-cell lineage malignancies.