Baum-Connes conjecture and semi-direct products of groups

Let Gamma = G x(r) N be the semi-direct product of two locally compact grou ps, and A a Gamma-algebra. We build a map from topological K-theory of Gamm a with coefficients in A to the one for G with coefficients in N x(r) A. Fo r Gamma a p-adic group equipped with a gamma element and N an amenable grou p, we prove that Gamma satisfies Baum-Connes conjecture with coefficients w hen G does. (C) Academie des Sciences/Elsevier, Paris.