We define background independent observables in a geometrical formulation as flat sections of the observable algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. A theory is then called background independent if such a flat (Fedosov) connection exists. We analyze the obstructions to preserve background independence at the quantum level for pure Yang-Mills theory and find that all potential obstructions can be removed by finite renormalization. Based on joint work with Mojtaba Taslimi Tehrani.