Intrinsic Taylor formula in fractional Holder space

We consider a class of non-local ultraparabolic Kolmogorov operators and we study suitable fractional Holder spaces that take into account the intrinsic sub-riemannian geometry induced by the operator. We prove a characterization relating the regularity along the vector fields to the existence of appropriate instrinsic Taylor formulas which extends in the non-local context the characterization given in the diffusive setting.