The Connes-Kasparov conjecture for almost connected groups and for linear p-adic groups
Publications Mathématiques de l'IHÉS, Tome 97 (2003), pp. 239-278.

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C * -algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero.

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     title = {The {Connes-Kasparov} conjecture for almost connected groups and for linear $p$-adic groups},
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Chabert, Jérôme; Echterhoff, Siegfried; Nest, Ryszard. The Connes-Kasparov conjecture for almost connected groups and for linear $p$-adic groups. Publications Mathématiques de l'IHÉS, Tome 97 (2003), pp. 239-278. doi : 10.1007/s10240-003-0014-2. http://www.numdam.org/articles/10.1007/s10240-003-0014-2/

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