  Diffeomorphism symmetry, the fundamental invariance of general relativity, is
generically broken under discretization. After discussing the meaning and
implications of diffeomorphism symmetry in the discrete, in particular for the
continuum limit, we introduce a perturbative framework to construct
discretizations with an exact notion of diffeomorphism symmetry. We will see
that for such a perturbative framework consistency conditions need to be
satisfied which enforce the preservation of the gauge symmetry to the
perturbative order under discussion. These consistency conditions will allow
structural investigations of diffeomorphism invariant discretizations.
