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.