This is a continuation of my previous talk. I will introduce affine Grassmannians parameterizing modifications of principal G-bundles on the projective line over a scheme. While the proof discussed in my first talk does not formally rely on affine Grassmannians, they were crucial in creating this proof.

Then I will explain how one can use affine Grassmannians to construct certain "exotic" principal bundles. This will explain why certain "naive" attempts at a proof of Grothendieck-Serre conjecture failed.