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.
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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. |
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