Cohomology algebras of 2-blocks of finite groups with defect groups of rank two

We shall calculate the cohomology algebras of 2-blocks of tame type and with wreathed defect groups; the cohomology algebra of B under consideration, in the sense of M. Linckelmann, is determined by particular B-subpairs, which we shall specify. In particular, depending our description of the cohomology algebras, we shall define “corestriction maps” between cohomology algebras of blocks which correspond under Brauer correspondence.