Let H be a Hopf algebra and A an H-comodule algebra. The case when A is a well-behaved extension of the algebra of coinvariants U, e.g. the theory of H-Galois extensions has been widely studied. On the contrary, we study the case when U is too small but the problem can be avoided using localizations. An Ore localization of a H-comodule algebra is compatible with the coaction if there is an induced H-comodule algebra structure on the localization. We consider finite sets of compatible Ore localizations A(s), covering A, where each localization A(s) has a structure of a smash product U(s)#H, and view this setup as an analogue of a locally trivial principal fibre bundle. We study a nontrivial class of natural examples related to quantum linear groups.