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We establish global Schauder estimates for integro-partial differentialequations (IPDE) driven by a possibly degenerate L\'evy Ornstein-Uhlenbeckoperator, both in the elliptic and parabolic setting, using some suitableanisotropic H\"older spaces. The class of operators we consider is composed bya linear drift plus a L\'evy operator that is comparable, in a suitable sense,with a possibly truncated stable operator. It includes for example, therelativistic, the tempered, the layered or the Lamperti stable operators. Ourmethod does not assume neither the symmetry of the L\'evy operator nor theinvariance for dilations of the linear part of the operator. Thanks to ourestimates, we prove in addition the well-posedness of the considered IPDE insuitable functional spaces. In the final section, we extend some of theseresults to more general operators involving non-linear, space-time dependentdrifts.

Schauder estimates for degenerate L\'evy Ornstein-Ulhenbeck operators