  We propose a regularized lattice model for quantum gravity purely formulated
in terms of fermions. The lattice action exhibits local Lorentz symmetry, and
the continuum limit is invariant under general coordinate transformations. The
metric arises as a composite field. Our lattice model involves no signature for
space and time, describing simultaneously a Minkowski or euclidean theory. It
is invariant both under Lorentz transformations and euclidean rotations. The
difference between space and time arises from expectation values of composite
fields. Our formulation includes local gauge symmetries beyond the generalized
Lorentz symmetry. The lattice construction can be employed for formulating
models with local gauge symmetries purely in terms of fermions
