Bivariant Hermitian K-theory and Karoubi's fundamental theorem

Let ? be a commutative ring with involution ? containing an element ? such that ?+??=1 and let Alg?? the category of ?-algebras equipped semilinear preserving homomorphisms. We construct triangulated kkh functor jh:Alg???kkh is homotopy invariant, matricially hermitian stable excisive universal initial these properties. prove version Karoubi's fundamental theorem holds in kkh. By property latter, this implies any H:Alg???T values which satisfies theorem. also bivariant 12-term exact sequence.