Lafforgue, V. Banach KK-theory and Baum-Connes conjecture. (English) Zbl 0997.19003 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press. 795-812 (2002). Summary: 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.For the entire collection see [Zbl 0993.00022]. Cited in 1 ReviewCited in 12 Documents MSC: 19K35 Kasparov theory (\(KK\)-theory) 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods 46L80 \(K\)-theory and operator algebras (including cyclic theory) Keywords:Kasparov’s KK-theory; Baum-Connes conjecture; discrete series PDFBibTeX XMLCite \textit{V. Lafforgue}, in: Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20--28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press; Singapore: World Scientific/distributor. 795--812 (2002; Zbl 0997.19003)