  Newstead and Ramanan conjectured the vanishing of the top (2g-1) Chern
classes of the moduli space of stable, odd degree vector bundles of rank 2 on a
Riemann surface of genus g. This was proved by Gieseker [G], while an analogue
in rank 3 was recently settled by Kiem and Li [KL]. We generalise this to the
vanishing of the top (g-1)r rational Chern classes of the moduli space M of
stable principal bundles with semi-simple structure group of rank r, whenever M
is a compact orbifold.
