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Following Serre's initial work, a number of authors have considered twists ofquadratic forms on a scheme Y by torsors of a finite group G, together withformulas for the Hasse-Witt invariants of the twisted form. In this paper wetake the base scheme Y to be affine and consider non-constant groups schemes G.There is a fundamental new feature in this case - in that the torsor may now beramified over Y. The natural framework for handling the case of a non-constantgroup scheme over the affine base is provided by the quadratic theory ofHopf-algebras.

Orthogonal representations of affine group schemes and twists of symmetric bundles