Do bosons feel spin frames?

In order to allow a coherent dynamical spinor-matter coupling in a previous paper of ours we introduced new variables to describe gravitational field, related to spin structures and called spin frames. A natural action of spa cetime diffeomorphisms on spin frames cannot be defined. Accordingly they m ust be treated as a sort of gauge fields, i.e. they must be considered to b e covariant with respect to automorphisms of some suitable principal bundle . In this paper we analyze what happens when general bosonic matter and gau ge fields interacting with gravity (described by spin frames) are considere d. As should be expected, such a theory reduces to a theory in which gravit y is described by means of a metric alone. Conserved quantities are also co nsidered in detail.