  Following Serre's initial work, a number of authors have considered twists of
quadratic forms on a scheme Y by torsors of a finite group G, together with
formulas for the Hasse-Witt invariants of the twisted form. In this paper we
take 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 be
ramified over Y. The natural framework for handling the case of a non-constant
group scheme over the affine base is provided by the quadratic theory of
Hopf-algebras.
