A transfer map is defined for finite surjective morphisms from integral schemes to a Noetherian integral normal base, for both chain complexes of sheaves and presheaves of spectra. The transfer is defined by adding up restriction maps along sections and thus sees only separable degrees, hence the name. The spectrum level transfer is a map from a direct image paired with the classifying space of a translation groupoid, and taking values in the original presheaf. More traditional transfer maps are recovered from global sections of the stack associated to this groupoid. These constructions can be made in the motivic stable category.