A. Kumjian et al., THE EQUIVARIANT BRAUER GROUPS OF COMMUTING FREE AND PROPER ACTIONS ARE ISOMORPHIC, Proceedings of the American Mathematical Society, 124(3), 1996, pp. 809-817
If X is a locally compact space which admits commuting free and proper
actions of locally compact groups G and H, then the Brauer groups Br-
H(G\X) and Br-G(X/H) are naturally isomorphic.