  We show in detail how the histories description of general relativity carries
representations of both the spacetime diffeomorphisms group and the Dirac
algebra of constraints. We show that the introduction of metric-dependent
equivariant foliations leads to the crucial result that the canonical
constraints are invariant under the action of spacetime diffeomorphisms.
Furthermore, there exists a representation of the group of generalised
spacetime mappings that are functionals of the four-metric: this is a spacetime
analogue of the group originally defined by Bergmann and Komar in the context
of the canonical formulation of general relativity. Finally, we discuss the
possible directions for the quantization of gravity in histories theory.
