  Using the Batalin-Vilkovisky technique and the background field method the
proof of gauge invariant renormalizability is elaborated for a generic model of
quantum gravity which is diffeomorphism invariant and has no other, potentially
anomalous, symmetries. The gauge invariant renormalizability means that in all
orders of loop expansion of the quantum effective action one can control
deformations of the generators of gauge transformations which leave such an
action invariant. In quantum gravity this means that one can maintain general
covariance of the divergent part of effective action when the mean quantum
field, ghosts and antifields are switched off.
