Représentations non unitaires, morphisme de Baum–Connes et complétions inconditionnelles

Abstract

We 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 discrete groups having Kazhdan’s property (T). We define a tensorisation by a non-unitary finite dimensional representation on the left-hand side 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].