The key ingredient for lattice regularized quantum gravity is diffeomorphism
symmetry. We formulate a lattice functional integral for quantum gravity in
terms of fermions. This allows for a diffeomorphism invariant functional
measure and avoids problems of boundedness of the action. We discuss the
concept of lattice diffeomorphism invariance. This is realized if the action
does not depend on the positioning of abstract lattice points on a continuous
manifold. Our formulation of lattice spinor gravity also realizes local Lorentz
symmetry. Furthermore, the Lorentz transformations are generalized such that
the functional integral describes simultaneously euclidean and Minkowski
signature. The difference between space and time arises as a dynamical effect
due to the expectation value of a collective metric field. The quantum
effective action for the metric is diffeomorphism invariant. Realistic gravity
can be obtained if this effective action admits a derivative expansion for long
wavelengths.Comment: 13 pages, proceedings 6th Aegean Summer School, Naxos 201