  A new exact renormalization group equation for the effective average action
of Euclidean quantum gravity is constructed. It is formulated in terms of the
component fields appearing in the transverse-traceless decomposition of the
metric. It facilitates both the construction of an appropriate infrared cutoff
and the projection of the renormalization group flow onto a large class of
truncated parameter spaces. The Einstein-Hilbert truncation is investigated in
detail and the fixed point structure of the resulting flow is analyzed. Both a
Gaussian and a non-Gaussian fixed point are found. If the non-Gaussian fixed
point is present in the exact theory, quantum Einstein gravity is likely to be
renormalizable at the nonperturbative level. In order to assess the reliability
of the truncation a comprehensive analysis of the scheme dependence of
universal quantities is performed. We find strong evidence supporting the
hypothesis that 4-dimensional Einstein gravity is asymptotically safe, i.e.
nonperturbatively renormalizable. The renormalization group improvement of the
graviton propagator suggests a kind of dimensional reduction from 4 to 2
dimensions when spacetime is probed at sub-Planckian length scales.
