  Hilbert space representations of the cross product *-algebras of the Hopf
*-algebra U_q(su_2) and its module *-algebras O(S^2_{qr}) of Podles spheres are
investigated and classified by describing the action of generators. The
representations are analyzed within two approaches. It is shown that the Hopf
*-algebra O(SU_q(2)) of the quantum group SU_q(2) decomposes into an orthogonal
sum of projective Hopf modules corresponding to irreducible integrable
*-representations of the cross product algebras and that each irreducible
integrable *-representation appears with multiplicity one. The projections of
these projective modules are computed. The decompositions of tensor products of
irreducible integrable *-representations with spin l representations of
U_q(su_2) are given. The invariant state h on O(S^2_{qr}) is studied in detail.
By passing to function algebras over the quantum spheres S^2_{qr}, we give
chart descriptions of quantum line bundles and describe the representations
from the first approach by means of the second approach.
