Rieffel deformation of homogeneous spaces

Let G1⊂G be a closed subgroup of a locally compact group G and let X=G/G1 be the quotient space of left cosets. Let X=(C0(X),ΔX) be the corresponding G-C∗-algebra where G=(C0(G),Δ). Suppose that Γ is a closed abelian subgroup of G1 and let Ψ be a 2-cocycle on the dual group . Let GΨ be the Rieffel deformation of G. Using the results of the previous paper of the author we may construct GΨ-C∗-algebra XΨ – the Rieffel deformation of X. On the other hand we may perform the Rieffel deformation of the subgroup G1 obtaining the closed quantum subgroup , which in turn, by the results of S. Vaes, leads to the GΨ-C∗-algebra . In this paper we show that . We also consider the case where Γ⊂G is not a subgroup of G1, for which we cannot construct the subgroup . Then generically XΨ cannot be identified with a quantum quotient. What may be shown is that it is a GΨ-simple object in the category of GΨ-C∗-algebras.