In algebraic geometry the coset spaces of affine algebraic
groups are in general not affine but rather only
quasiprojective varieties. Hence the affine coordinate
ring of a coset space does not adequately represent
that space in general and one uses a sheaf-theoretic picture instead.
We propose a crude extension of such a sheaf-theoretic description
to noncommutative Hopf algebras using covers
by well-behaved Ore localizations. A nontrivial example
where such a program has been realized involves quantized
ring of regular functions on SL(n) modulo quantum parabolics.
For that aim we use quantum Gauss decompositions, Weyl group and
calculations with quantum minors.