  We show how H\"older estimates for Feller semigroups can be used to obtain
regularity results for solutions to the Poisson equation $Af=g$ associated with
the (extended) infinitesimal generator $A$ of a Feller process. The regularity
of $f$ is described in terms of H\"older-Zygmund spaces of variable order and,
moreover, we establish Schauder estimates. Since H\"{o}lder estimates for
Feller semigroups have been intensively studied in the last years, our results
apply to a wide class of Feller processes, e.g. random time changes of L\'evy
processes and solutions to L\'evy-driven stochastic differential equations.
Most prominently, we establish Schauder estimates for the Poisson equation
associated with the fractional Laplacian of variable order. As a by-product, we
obtain new regularity estimates for semigroups associated with stable-like
processes.
