  We show that for a SU(N) Yang-Mills theory the classical background-quantum
splitting is non-trivially deformed at the quantum level by a canonical
transformation with respect to the Batalin-Vilkovisky bracket associated with
the Slavnov-Taylor identity of the theory. This canonical transformation acts
on all the fields (including the ghosts) and antifields; it uniquely fixes the
dependence on the background field of all the one-particle irreducible Green's
functions of the theory at hand. The approach is valid both at the perturbative
and non-perturbative level, being based solely on symmetry requirements. As a
practical application, we derive the renormalization group equation in the
presence of a generic background and apply it in the case of a SU(2) instanton.
Finally, we explicitly calculate the one-loop deformation of the
background-quantum splitting in lowest order in the instanton background.
