Stabilization of the Witt group

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.