Split Weyl transformations in quantum gravity

We discuss various realizations of the Weyl group in the background field expansion of quantum gravity, in the presence of a cutoff, as required in applications of the functional renormalization group. In order to study the background–dependence, special attention is given to split gauge transformations, which act on the background field and fluctuation keeping the total metric unchanged. The results generalize previous works on global and local scale transformations.