Algebraic $K_0$ of the Quantum Sphere and Noncommutative Index Theorem
  The Noncommutative Index Theorem is used to prove that the Chern character of quantum Hopf line bundles over the standard Podles quantum sphere equals the winding number of the representations defining these bundles. This result gives an estimate of the positive cone of the algebraic $K_0$ of the standard quantum sphere. 
Piotr M. Hajac