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

Corestriction for algebras with group action