  Using the Cartan formulation of General Relativity, we construct a well
defined lattice-regularized theory capable to describe large non-perturbative
quantum fluctuations of the frame field (or the metric) and of the spin
connection. To that end we need to present the tetrad by a composite field
built as a bilinear combination of fermion fields. The theory is explicitly
invariant under local Lorentz transformations and, in the continuum limit,
under general covariant transformations, or diffeomorphisms. Being well defined
for large and fast varying fields at the ultraviolet cutoff, the theory
simultaneously has chances of reproducing standard General Relativity in the
infrared continuum limit. The present regularization of quantum gravity opens
new possibilities of its unification with the Standard Model.
