Even more is true: denote by $R(G)$ the ring of homotopy classes of finite-dimensional representations of $G$ (not necessarily unitary ones); then there is a module action of $R(G)$ on $K_(C^_rG)$. K_*(C_r^*G)$. See my memoir: Les fibr\'es en th\'eorie de Kasparov'', Acad. Royale de Belgique, M\'emoire Classe des Sciences, 2eme s\'erie, T. XLV, Fasc.6, 1988. 1 Even more is true: denote by$R(G)$the ring of homotopy classes of finite-dimensional representations of$G$(not necessarily unitary ones); then there is a module action of$R(G)$on$K_(C^_rG)\$. See my memoir: Les fibr\'es en th\'eorie de Kasparov'', Acad. Royale de Belgique, M\'emoire Classe des Sciences, 2eme s\'erie, T. XLV, Fasc.6, 1988.