process

178 C. VoigtKK-theory [16]. Hence, roughly speaking, the theory in [2], [22] only recovers thedegree zero part of the group cohomology. A similar remark applies to the homologygroups defined in [1].We mention that Akbarbour and Khalkhali have obtained an analogue of the Green–Julg isomorphismHP H .C;A/Š HP .A Ì H/if H is semisimple and A is a unital H -algebra [1]. This result holds in fact moregenerally in the case that H is the convolution algebra of a compact quantum groupand A is an arbitrary H -algebra. Similarly, there is a dual versionHP H .A; C/ Š HP .A Ì H/of the Green–Julg theorem for the convolution algebras of discrete quantum groups.The latter generalizes the identification of equivariant periodic cyclic cohomology fordiscrete groups mentioned above. These results will be discussed elsewhere.References[1] R. Akbarpour, M. Khalkhali, Hopf algebra equivariant cyclic homology and cyclic cohomologyof crossed product algebras, J. Reine Angew. Math. 559 (2003), 137–152.[2] R. Akbarpour, M. Khalkhali, Equivariant cyclic cohomology of H -algebras, K-theory 29(2003), 231–252.[3] S. Baaj, G. Skandalis, C -algèbres de Hopf et théorie de Kasparov équivariante, K-theory2 (1989), 683–721.[4] J. Block, E. Getzler, Equivariant cyclic homology and equivariant differential forms, Ann.Sci. École. Norm. Sup. 27 (1994), 493–527.[5] J.-L. Brylinski, Algebras associated with group actions and their homology, Brown Universitypreprint, 1986.[6] J.-L. Brylinski, Cyclic homology and equivariant theories, Ann. Inst. Fourier 37 (1987),15–28.[7] A. Connes, Noncommutative Geometry, Academic Press, 1994.[8] J. Cuntz, D. Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995),251–289.[9] J. Cuntz, D. Quillen, Cyclic homology and nonsingularity, J. Amer. Math. Soc. 8 (1995),373–442.[10] J. Cuntz, D. Quillen, Excision in bivariant periodic cyclic cohomology, Invent. Math. 127(1997), 67 - 98.[11] B. Drabant, A. van Daele, Y. Zhang, Actions of multiplier Hopf algebras, Comm. Algebra27 (1999), 4117–4172.[12] P. Hajac,M. Khalkhali, B. Rangipour, Y. Sommerhäuser, Stable anti-Yetter-Drinfeld modules,C. R. Acad. Sci. Paris 338 (2004), 587–590.[13] P. Hajac,M. Khalkhali, B. Rangipour, Y. Sommerhäuser, Hopf-cyclic homology and cohomologywith coefficients, C. R. Acad. Sci. Paris 338 (2004), 667–672.