  We apply the ``consistent discretization'' approach to general relativity
leaving the spatial slices continuous. The resulting theory is free of the
diffeomorphism and Hamiltonian constraints, but one can impose the
diffeomorphism constraint to reduce its space of solutions and the constraint
is preserved exactly under the discrete evolution. One ends up with a theory
that has as physical space what is usually considered the kinematical space of
loop quantum geometry, given by diffeomorphism invariant spin networks endowed
with appropriate rigorously defined diffeomorphism invariant measures and inner
products. The dynamics can be implemented as a unitary transformation and the
problem of time explicitly solved or at least reduced to as a numerical
problem. We exhibit the technique explicitly in 2+1 dimensional gravity.
