  We introduce intrinsic Sobolev-Slobodeckij spaces for a class of
ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander
condition. We prove continuous embeddings into Lorentz and intrinsic H\"older
spaces. We also prove approximation and interpolation inequalities by means of
an intrinsic Taylor expansion, extending analogous results for H\"older spaces.
The embedding at first order is proved by adapting a method by Luc Tartar which
only exploits scaling properties of the intrinsic quasi-norm, while for higher
orders we use uniform kernel estimates.
