  In this paper we outline a recent construction of a Chern-Weil isomorphism
for the equivariant Brauer group of $\mathbb R^n$ actions on a principal torus
bundle, where the target for this isomorphism is a "dimensionally reduced"
\vCech cohomology group. Using this latter group, we demonstrate how to extend
the induced algebra construction to algebras with a non-trivial bundle as their
spectrum.
