Rigidity and Vanishing Theorems in K-Theory II
  We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a family of almost complex manifolds. 
Kefeng Liu, Xiaonan Ma, Weiping Zhang