The Baum-Connes conjecture and discrete group actions on trees

We introduce a property (BC') for discrete groups, which we prove to imply the Baum-Connes conjecture with coefficients and the K-amenability of the group. Then, we show that if Gamma is a discrete group which acts on a tree X such that X/Gamma is compact, and the stabilizers of the vertices and the stabilizers of the edges satisfy (BC'), then Gamma itself satisfies (BC'). Finally, we indicate a couple of applications.