  A geometric formulation of Wilson's exact renormalisation group is presented
based on a gauge invariant ultraviolet regularisation scheme without the
introduction of a background field. This allows for a manifestly background
independent approach to quantum gravity and gauge theories in the continuum.
The regularisation is a geometric variant of Slavnov's scheme consisting of a
modified action, which suppresses high momentum modes, supplemented by
Pauli-Villars determinants in the path integral measure. An exact
renormalisation group flow equation for the Wilsonian effective action is
derived by requiring that the path integral is invariant under a change in the
cutoff scale while preserving quasi-locality. The renormalisation group flow is
defined directly on the space of gauge invariant actions without the need to
fix the gauge. We show that the one-loop beta function in Yang-Mills and the
one-loop divergencies of General Relativity can be calculated without fixing
the gauge. As a first non-perturbative application we find the form of the
Yang-Mills beta function within a simple truncation of the Wilsonian effective
action.
