The Connes-Kasparov conjecture for almost connected groups and for linear p -adic groups

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.