Noncommutative principal bundles on projective bases

The notion of noncommutative principal bundle is not as well understood as that of noncommutative vector bundle. Main examples, like the noncommutative instanton bundle, are algebraically understood as Hopf-Galois extensions. This definition is particularly useful when the noncommutative base space is affine (the function algebra being given in terms of generators and relations). We relax it by presenting a sheaf theoretic approach that allows to consider noncommutative principal bundles over non affine base spaces; examples include projective spaces.