  Let G be a locally compact group and rho a non-unitary finite dimensional
representation of G. We consider tensor products of rho by some unitary
representations of G in order to define two Banach algebras analogous to the
group C*-algebras, C*(G) and C*_r(G). We calculate the K-theory of such
algebras for a large class of groups satisfying the Baum-Connes conjecture.
