2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159900We show that the Baum-Connes morphism twisted by a non-unitary representation, defined in [GA08], is an isomorphism for a large class of groups satisfying the Baum-Connes conjecture. Such class contains all the real semi-simple Lie groups, all hyperbolic groups and many infinite discret groups having Kazhdan's property (T). We define a tensorisation by a non-unitary finite dimensional representation on the left handside of the Baum-Connes morphism and we show that its analogue in K-theory must be defined on the K-theory of the twisted group algebras introduced in [GA07b].29 pages, in frenchK-Theory and HomologyOperator Algebras22D12, 22D15, 46L80, 19K35text