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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.