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The most momentous requirement a quantum theory of gravity must satisfy isBackground Independence, necessitating in particular an ab initio derivation ofthe arena all non-gravitational physics takes place in, namely spacetime. Usingthe background field technique, this requirement translates into the conditionof an unbroken split-symmetry connecting the (quantized) metric fluctuations tothe (classical) background metric. If the regularization scheme used violatessplit-symmetry during the quantization process it is mandatory to restore it inthe end at the level of observable physics. In this paper we present a detailedinvestigation of split-symmetry breaking and restoration within the EffectiveAverage Action (EAA) approach to Quantum Einstein Gravity (QEG) with a specialemphasis on the Asymptotic Safety conjecture. In particular we demonstrate forthe first time in a non-trivial setting that the two key requirements ofBackground Independence and Asymptotic Safety can be satisfied simultaneously.Carefully disentangling fluctuation and background fields, we employ a`bi-metric' ansatz for the EAA and project the flow generated by its functionalrenormalization group equation on a truncated theory space spanned by twoseparate Einstein-Hilbert actions for the dynamical and the background metric,respectively. A new powerful method is used to derive the correspondingrenormalization group (RG) equations for the Newton- and cosmological constant,both in the dynamical and the background sector. We classify and analyze theirsolutions in detail, determine their fixed point structure, and identify anattractor mechanism which turns out instrumental in the split-symmetryrestoration. We show that there exists a subset of RG trajectories which areboth asymptotically safe and split-symmetry restoring. We conclude that thenext generation of truncations must be bi-metric.

En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions