  We investigate the gauge symmetry and gauge fixing dependence properties of
the effective average action for quantum gravity models of general form. Using
the background field formalism and the standard BRST-based arguments, one can
establish the special class of regulator functions that preserves the
background field symmetry of the effective average action. Unfortunately,
regardless the gauge symmetry is preserved at the quantum level, the
non-invariance of the regulator action under the global BRST transformations
leads to the gauge fixing dependence even under the use of the on-shell
conditions.
