  The goal of the present paper is the calculation of the equivariant twisted
K-theory of a compact Lie group which acts on itself by conjugations, and
elements of a TQFT-structure on the twisted K-groups. These results are
originally due to D.S.Freed, M.J.Hopkins and C.Teleman. In this paper we redo
their calculations in the framework of topological and differentiable stacks.
We also show how moduli spaces of flat connections on surfaces give rise to
trivializations of twists.
