  In Parts I and II of the work (gr-qc/9405013, 9407032), we have shown that
gravity is {\it sui generis} a Higgs field corresponding to spontaneous
symmetry breaking when the fermion matter admits only the Lorentz subgroup of
world symmetries of the geometric arena. From the mathematical viewpoint, the
Higgs nature of gravity issues from the fact that different gravitational
fields are responsible for nonequivalent representations of cotangent vectors
to a world manifold by $\gamma$-matrices on spinor bundles. It follows that
gravitational fields fail to form an affine space modelled on a linear space of
deviations of some background field. In other words, even weak gravitational
fields do not satisfy the superposition principle and, in particular, can not
be quantized by usual methods. At the same time, one can examine superposable
deviations $\sigma$ of a gravitational field $h$ so that $h+\sigma$ fails to be
a gravitational field. These deviations are provided with the adequate
mathematical description in the framework of the affine group gauge theory in
dislocated manifolds, and their Lagrangian densities differ from the familiar
gravitational ones. They make contribution to the standard gravitational
effects, e.g., modify Newton's gravitational potential.
