Push-forwards in oriented cohomology theories of algebraic varieties: II

This preprint contains proofs of the results anounced in [PS] in the part concerning the construction of push-forwards for an oriented cohomology theory. It is constructed one-to-one correspondences between orientations, Chern structures, Thom structures and integrations on a given ring cohomology theory. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theory and by other examples. Other terms often used in the literature for push-forwards are Gysin homomorphisms, trace homomorphisms, corestriction homomorphisms, transfers.