Algebraic construction and properties of Hermitian analogs of $K$-theory over rings with involution from the viewpoint of Hamiltonian formalism. applications to differential topology and the theory of characteristic classes. II

The present paper is an immediate continuation of the author's paper [22]. Except in the last section, it is implicitly assumed here, as in [22], that the underlying ring contains 1/2 and all the theorems relate to the theory $U\otimes Z[1/2]$ without further comment.