  The report below describes the applications of Banach KK-theory to a
conjecture of P. Baum and A. Connes about the K-theory of group $C^*$-algebras,
and a new proof of the classification by Harish-Chandra, the construction by
Parthasarathy and the exhaustion by Atiyah and Schmid of the discrete series
representations of connected semi-simple Lie groups.
