  The geometro-stochastic method of quantization provides a framework for
quantum general relativity, in which the principal frame bundles of local
Lorentz frames that underlie the fibre-theoretical approach to classical
general relativity are replaced by Poincar\'e-covariant quantum frame bundles.
In the semiclassical regime for quantum field theory in curved spacetime, where
the gravitational field is not quantized, the elements of these local quantum
frames are generalized coherent states, which emerge naturally from phase space
representations of the Poincar\'e group. Due to their informational
completeness, these quantum frames are capable of taking over the role played
by complete sets of observables in conventional quantum theory. The propagation
of quantum-geometric fields proceeds by path integral methods, based on
parallel transport along broken paths consisting of arcs of geodesics of the
Levi-Civita connection. The formulation of quantum gravity within this
framework necessitates the transition to quantum superframe bundles and a
quantum gravitational supergroup capable of incorporating diffeomorphism
invariance into the framework. This results in a geometric version of quantum
gravity which shares some conceptual features with covariant as well as with
canonical gravity, but which avoids the foundational and the mathematical
difficulties encountered by these two approaches.
