  Like the Higgs bundles on a Riemann surface who played an important role in
the study of representation of the fundamental group of the surface, the
parabolic Higgs bundles play also their importance in the study of the
fundamental group but of punctured surface. In this paper, we shall give an
algorithm to calculate the (virtual) motive (i.e in a suitable Grothendieck
ring) of the moduli spaces of parabolic Higgs bundles of fixed rank, fixed
degree and fixed parabolic structure, using localization with respect to the
circle action.
