Gauge groups and bialgebroids

We study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as quantization gauge groupoid classical bundle. show that group is isomorphic to bisections bialgebroid, and we give crossed module structure for automorphisms bialgebroid. Examples illustrating these constructions include: Galois objects Taft algebras, monopole over quantum spheres not faithfully flat Hopf--Galois extension commutative algebras. The latter two examples have in fact Hopf algebroid suitable invertible antipode.