caa a22 4500 378921037 CHVBK 20180305123605.0 cr unu---uuuuu 161128e200406 xx s 000 0 eng 10.1515/GMJ.2004.283 doi (NATIONALLICENCE)gruyter-10.1515/GMJ.2004.283 Kandelaki T. A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 0193, Georgia. E-mail: kandel@rmi.acnet.ge Karoubi-Villamayor K-Theory, Weakly Stable C*-Categoroids, and KK-Theory [Elektronische Daten] [T. Kandelaki] The aim of the paper is to give, according to Karoubi-Villamayor K-groups, an interpretation of Kasparov KK-groups. It continues the study of KK-theory by the methods of K-theory, focusing attention on the problem posed and discussed in the author's papers published in 2000 and 2001. But the methods used in those papers are based on the excision property and Morita invariance of algebraic and topological K-theories on the category of C*-algebras, which are not applicable to Karoubi-Villamayor K-theory, since excision holds only for some sub class of short exact sequences of C*-algebras. In this paper we introduce and study a weak stability property of the C*-category Rep(A, B), which is the key to our problem. © Heldermann Verlag Karoubi-Villamayor K-theory of C*-categories nationallicence Kasparov KK-theory nationallicence Georgian Mathematical Journal Walter de Gruyter GmbH & Co. KG 11/2(2004-06), 283-299 1072-947X 11:2<283 2004 11 GMJ https://doi.org/10.1515/GMJ.2004.283 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/GMJ.2004.283 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kandelaki T. A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 0193, Georgia. E-mail: kandel@rmi.acnet.ge NATIONALLICENCE 773 0- Georgian Mathematical Journal Walter de Gruyter GmbH & Co. KG 11/2(2004-06), 283-299 1072-947X 11:2<283 2004 11 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter