The structure of the Brauer group and crossed products of C-0(X)-linear group actions on C-0(X; K)

For a second countable locally compact group G and a second countable local ly compact space X let Br-G (X) denote the equivariant Brauer group (for th e trivial G-space X) consisting of all Morita equivalence classes of spectr um fixing actions of G on continuous-trace C*-algebras A with spectrum (A) over cap = X. Extending recent results of several authors, we give a comple te description of Br-G (X) in terms of group cohomology of G and Cech cohom ology of X. Moreover, if G has a splitting group H in the sense of Calvin M oore, we give a complete description of the C-0(X)-bundle structure of the crossed product A (X)(alpha) G in terms of the topological data associated to the given action alpha : G --> Aut A and the bundle structure of the gro up C*-algebra C*(H) of H.