Geometric Baum-Connes assembly map for twisted differentiable stacks (Q2811180)

The authors construct the geometric Baum-Connes assembly map for twisted Lie groupoids. For this construction, they use geometric deformation groupoids to give, in particular, a geometric construction of the associated pushforward maps and to establish the functoriality. The main results in this paper are the definition of the geometric twisted K-homology groups and the construction of the assembly map.NEWLINENEWLINEThe authors also prove the Morita invariance of the assembly map, obtaining in this way a precise meaning to the twisted geometric assembly map for differentiable stacks. This point is essential since, in practice, one usually changes the groupoid model by the Morita equivalent one.