Behavior of R-groups for p-adic inner forms of quasi-split special unitary groups

Abstract. We study R-groups for p-adic inner forms of quasi-split special unitary groups. We prove Arthur’s conjecture, the isomorphism between the Knapp-Stein R-group and the Langlands-Arthur R-group, for quasi-split special unitary groups and their inner forms. Furthermore, we investigate the invariance of the Knapp-Stein R-group within L-packets and between inner forms. This work is applied to transferring known results in the second-named author’s earlier work for quasi-split special unitary groups to their non-quasi-split inner forms.