  We calculate the Euler characteristic of associated vector bundles over the
moduli spaces of stable parabolic bundles on smooth curves. Our method is based
on a wall-crossing technique from Geometric Invariant Theory, certain iterated
residue calculus and the tautological Hecke correspondence. Our work was
motivated by the results of Teleman and Woodward on the index of K-theory
classes on moduli stacks.
