Stable anti-Yetter-Drinfeld modules
  We define and study a class of entwined modules (stable anti-Yetter-Drinfeld modules) that serve as coefficients for the Hopf-cyclic homology and cohomology. In particular, we explain their relationship with Yetter-Drinfeld modules and Drinfeld doubles. Among sources of examples of stable anti-Yetter-Drinfeld modules, we find Hopf-Galois extensions with a flipped version of the Miyashita-Ulbrich action. 
Piotr M. Hajac, Masoud Khalkhali, Bahram Rangipour, Yorck   Sommerhaeuser