  Alain Connes and Nigel Higson pointed out in the 1990s that the
Connes-Kasparov "conjecture"' for the K-theory of reduced groupe
$C^\ast$-algebras seemed, in the case of reductive Lie groups, to be a
cohomological echo of a conjecture of George Mackey concerning the rigidity of
representation theory along the deformation from a reductive Lie group to its
Cartan motion group. For complex semisimple groups, Nigel Higson established in
2008 that Mackey's analogy is a real phenomenon and does lead to a simple proof
of the Connes-Kasparov isomorphism. We here turn to more general reductive
groups and use our recent work on Mackey's proposal, together with Higson's
work, to obtain a new proof of the Connes-Kasparov isomorphism.
