  We establish global Schauder estimates for integro-partial differential
equations (IPDE) driven by a possibly degenerate L\'evy Ornstein-Uhlenbeck
operator, both in the elliptic and parabolic setting, using some suitable
anisotropic H\"older spaces. The class of operators we consider is composed by
a linear drift plus a L\'evy operator that is comparable, in a suitable sense,
with a possibly truncated stable operator. It includes for example, the
relativistic, the tempered, the layered or the Lamperti stable operators. Our
method does not assume neither the symmetry of the L\'evy operator nor the
invariance for dilations of the linear part of the operator. Thanks to our
estimates, we prove in addition the well-posedness of the considered IPDE in
suitable functional spaces. In the final section, we extend some of these
results to more general operators involving non-linear, space-time dependent
drifts.
