  We prove that if the classical Baum-Connes conjecture in complex K-theory is
true (for a given discrete group G), then the conjecture is also true in the
real case (for the same group G). The essential ingredients of the proof are
the descent theorem in topological K-theory (math.KT/0509396) and a Paschke
duality for C*-algebras proved by John Roe (Q.J. Math. 55 (2004) 325-331).
According to S. Stolz, this result is linked with the existence of a Riemannian
metric of positive scalar curvature on a compact connected spin manifold with G
as fundamental group.
