A preparation of autologous T-lymphocytes that are genetically modified to express a chimeric antigen receptor (CAR) for a modified and inactivated form of the type II transmembrane protein human natural-killer group 2, member D receptor protein (NKG2D; KLRK1), that can be used for potential immunostimulating and antineoplastic activities upon activation in vivo. Upon infusion back into the patient, autologous NKG2D CAR-expressing T-lymphocytes ASP2802 are inert. Upon subsequent administration of MA-20 (ASP101G; MicAbody), a bispecific adaptor molecule composed of an anti-CD20 antibody linked to a UL16-binding protein (ULBP) 2 ligand, the anti-CD20 antibody moiety of MA-20 targets and binds to CD20-expressing tumor cells and the ULBP2 ligand targets and binds to the NKG2D CAR moiety of the convertible CAR T-cells ASP2802, thereby activating the inactivated CAR T-cells, which induce selective toxicity in and lysis of 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.