Equivariant central simple graded algebras and the equivariant Brauer–Wall group

We consider central simple -graded algebras over a field K of characteristic ≠2 acted on by a group G via graded automorphisms. The equivariant Brauer–Wall group BW(K,G) is defined by means of an equivalence relation among these algebras. Its structure as an Abelian group is completely determined using the known structure of the Brauer–Wall group BW(K) due to C.T.C. Wall. It is also shown that there is a homomorphism W(K,G)→BW(K,G) where W(K,G) is the equivariant Witt group defined by A. Fröhlich and A.M. McEvett.