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

On the motives of moduli of parabolic chains and parabolic Higgs bundles