  The current understanding of renormalization in quantum gravity (QG) is based
on the fact that UV divergences of effective actions in the covariant QG models
are covariant local expressions. This fundamental statement plays a central
role in QG and, therefore, it is important to prove it for the widest possible
range of the QG theories. Using the Batalin-Vilkovisky technique and the
background field method, we elaborate the proof of gauge invariant
renormalizability for a generic model of quantum gravity that is diffeomorphism
invariant and does not have additional, potentially anomalous, symmetries.
