Moore cohomology and central twisted crossed product C*-algebras

Let G be a locally compact second countable group, let X be a locally compact second countable Hausdorff space, and view C(X, T) as a trivial G-module. For G countable discrete abelian, we construct an isomorphism between the Moore cohomology group H-n(G,C(X,T)) and the direct sum Ext(H-n-1(G),H-1(beta X,Z)) + C(X,H-n(G, T)); here H-1(beta X,Z) denotes the first Cech cohomology group of the Stone-Cech compactification of X, beta X, with integer coefficients. For more general locally compact second countable groups G, we discuss the relationship between the Moore group HZ(G, C(X,T)), the set of exterior equivalence classes of element-wise inner actions of G on the stable continuous trace C*-algebra C-0(X) x K, and the equivariant Brauer group Br-G(X) of Crocker, Kumjian, Raeburn, and Williams. For countable discrete abelian G acting trivially on X, we construct an isomorphism Br-G(X) congruent to H-3(X, Z) + HP(X, G) + C(X,H-2(G, T)); here HP(X, G) is the group of equivalence classes of principal G bundles over X first considered by Raeburn and Williams.