Associated to the standard SUq(n) R-matrices, we introduce quantum sph
eres S-q(2n-1), projective quantum spaces CPqn-1, and quantum Grassman
n manifolds G(k)(C-q(n)). These algebras are shown to be homogeneous s
paces of standard quantum groups and are also quantum principle bundle
s in the sense of T. Brzezinski and S. Majid.