  We calculate the twisted Hochschild and cyclic homology (in the sense of
Kustermans, Murphy and Tuset) of all Podles quantum spheres relative to
arbitary automorphisms. Our calculations are based on a free resolution due to
Masuda, Nakagami and Watanabe. The dimension drop in Hochschild homology can be
overcome by twisting by automorphisms induced from the canonical modular
automorphism associated to the Haar state on quantum SU(2). We specialize our
results to the standard quantum sphere, and identify the class in twisted
cyclic cohomology of the 2-cocycle discovered by Schmuedgen and Wagner
corresponding to the distinguished covariant differential calculus found by
Podles.
