Abstract We study bundle gerbes on manifolds M that carry an action of a connected Lie group G . show these data give rise to smooth 2-group extension by the hermitean line bundles This classifies equivariant structures gerbe, and its non-triviality poses obstruction existence structures. present new global approach parallel transport gerbe with connection, use it alternative construction this ...

Given a normal subgroup bundle A of the isotropy groupoid ?, we obtain twisted action quotient ?/A on group C?-algebras determined by whose crossed product recovers C?-algebra C?(?). Restricting to case where is abelian, describe C?(?) as associated T-groupoid over tranformation obtained from canonical Pontryagin dual space A. We give some illustrative examples this result.

Let A and B be separable C∗-algebras, A unital and B stable. It is shown that there is a natural six-terms exact sequence which relates the group which arises by considering all semi-split extensions of A by B to the group which arises by restricting the attention to unital semi-split extensions of A by B. The six-terms exact sequence is an unpublished result of G. Skandalis. Let A,B be separab...