I will describe a principle bundle by a groupoid, a gerbe on a principle bundle by a twisting of the groupoid multiplication, and a group action on such a gerbe (which is compatible with the principle bundle action) by a 2-cocycle in equivariant groupoid cohomology. This description of an "equivariant gerbe" on a principle bundle allows for two constructions. The first is a Fourier type isomorphism from the groupoid algebra of the equivariant gerbe to another interesting groupoid algebra. Here the principle bundle should be a bundle of abelian groups. The second construction is a deformed version of the important Morita equivalence called Mackey-Rieffel imprimitivity. A certain composition of these two constructions, when applied to a gerbe on a principle torus bundle, reveals itself as the T-duality that has been much studied by Mathai, Raeburn, Rosenbenberg, Williams and others!