The Frobenius Map and Locally Trivial Principal Bundles

Given a connected reductive group G, Serre had conjectured that any rationally trivial principal G-bundle on a smooth variety is
locally trivial in the Zariski topology. This was proved by Colliot-Thélène, Ojanguren and Raghunathan. We give a quick proof using semistable vector bundles (joint work with S. Subramanian).