Abstract (EN)

We give a new representation-theory based proof of the Connes-Kasparov conjecture for the K-theory of reduced C*-algebras of real reductive Lie groups. Our main tool is a natural correspondence between the tempered representation theory of such a group and that of its Cartan motion group, a semidirect product whose unitary dual and reduced C*-algebra are much more tractable. With that tool in hand, our proof is a natural adaptation of that given by Nigel Higson's work in the complex semi-simple case.