Corestriction for algebras with group action

We define a corestriction map for equivariant Brauer groups in the sense of Fr\"ohlich and Wall, which contain as a special case the Brauer-Clifford groups introduced by Turull. We show that this corestriction map has similar properties as the corestriction map in group cohomology (especially Galois cohomology). In particular, composing corestriction and restriction associated to a subgroup $H\leq G$ amounts to powering with the index $\lvert G:H \rvert$.