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. I

The complicated and intricate algebraic material in smooth topology (the theory of surgery) does not fit into the already existing concepts of stable algebra. It turns out that the systematization of this material is most naturally carried through from the point of view of an algebraic version of the hamiltonian formalism over rings with involution. The present article is devoted to this task. The first part contains a development of the algebraic concepts.