2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67203The 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.Operator Algebras19K35, 22E45, 46L80text