  Denef and Loeser defined a map from the Grothendieck ring of sets definable
in pseudo-finite fields to the Grothendieck ring of Chow motives, thus enabling
to apply any cohomological invariant to these sets. We generalize this to
perfect, pseudo algebraically closed fields with pro-cyclic Galois group. In
addition, we define some maps between different Grothendieck rings of definable
sets which provide additional information, not contained in the associated
motive. In particular we infer that the map of Denef-Loeser is not injective.
