Differential forms on moduli spaces of principal bundles

Let X be a smooth projective variety, G a connected reductive algebraic group, and let M_G be a moduli space of stable principal G-bundles over X. By defining a suitable local version of the Atiyah class of a family of principal bundles and applying it to a (locally defined) universal family of principal G-bundles over M_G, we are able to construct, in a natural way, closed differential forms on the moduli space M_G. We remark that no assumption about the smoothness of the moduli spaces is made.