  We present a geometric construction of push-forward maps along projective
morphisms for cohomology theories representable in the stable motivic homotopy
category assuming that the element corresponding to the stable Hopf map is
inverted in the coefficient ring of the theory. The construction is parallel to
the one given by A. Nenashev for derived Witt groups. Along the way we
introduce cohomology groups twisted by a formal difference of vector bundles as
cohomology groups of a certain Thom space and compute twisted cohomology groups
of projective spaces.
