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Motivated by recent evidence indicating that Quantum Einstein Gravity (QEG)might be nonperturbatively renormalizable, the exact renormalization groupequation of QEG is evaluated in a truncation of theory space which generalizesthe Einstein-Hilbert truncation by the inclusion of a higher-derivative term$(R^2)$. The beta-functions describing the renormalization group flow of thecosmological constant, Newton's constant, and the $R^2$-coupling are computedexplicitly. The fixed point (FP) properties of the 3-dimensional flow areinvestigated, and they are confronted with those of the 2-dimensionalEinstein-Hilbert flow. The non-Gaussian FP predicted by the latter is found togeneralize to a FP on the enlarged theory space. In order to test thereliability of the $R^2$-truncation near this FP we analyze the residual schemedependence of various universal quantities; it turns out to be very weak. Thetwo truncations are compared in detail, and their numerical predictions arefound to agree with a suprisingly high precision. Due to the consistency of theresults it appears increasingly unlikely that the non-Gaussian FP is anartifact of the truncation. If it is present in the exact theory QEG isprobably nonperturbatively renormalizable and ``asymptotically safe''. Wediscuss how the conformal factor problem of Euclidean gravity manifests itselfin the exact renormalization group approach and show that, in the$R^2$-truncation, the investigation of the FP is not afflicted with thisproblem. Also the Gaussian FP of the Einstein-Hilbert truncation is analyzed;it turns out that it does not generalize to a corresponding FP on the enlargedtheory space.Comment: 107 pages, latex, 9 figure

Flow equation of quantum Einstein gravity in a higher-derivative truncation