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A fibre product construction is used to give a description of quantum linebundles over the generic Podles spheres by gluing two quantum discs along theirboundaries. Representatives of the corresponding $K_0$-classes are given interms of 1-dimensional projections belonging to the C*-algebra, and in terms ofanalogues of the classical Bott projections. The $K_0$-classes of quantum linebundles derived from the generic Hopf fibration of quantum SU(2) are determinedand the index pairing is computed. It is argued that taking the projectionsobtained from the fibre product construction yields a significantsimplification of earlier index computations.

Fibre product approach to index pairings for the generic Hopf fibration of SU_q(2)