  In this paper we construct a Chern-Weil isomorphism for the equivariant
Brauer group of R^n-actions on a principal torus bundle, where the target for
this isomorphism is a "dimensionally reduced" Cech cohomology group. From this
point of view, the usual forgetful functor takes the form of a connecting
homomorphism in a long exact sequence in dimensionally reduced cohomology.
