  Using an idea due to R.Thomason, we define a "homology theory" on the
category of rings which satisfies excision, exactness, homotopy (in the
algebraic sense) and periodicity of order 4. For regular noetherian rings, we
find P. Balmer's higher Witt groups. For more general rings, this homology
isomorphic to the KT-theory of J. Hornbostel, inspired by the work of B.
Williams. For real or complex C*-algebras, we recover - up to 2 torsion -
topological K-theory.
