[The preprint has been withdrawn by the author, and the files have been deleted.]
To any small triangulated category a K-theory K(T) is associated. We
introduce the class of W-triangulated categories and prove the appriximation,
additivity and localization theorems for them. The most important for
applications examples of W-triangulated categories are derived categories and
the stable category of a locally finite group. We also show that Quillen's
K-theory of an exact category E is homotopy equivalent to the K-theory for
the bounded derived category of E.
Important addendum from the author, March 16, 2002:
Marco Schlichting has constructed counter-examples (the preprint is available
at his homepage) which contradict author's preprint 'K-theory for
triangulated categories'. Thus main results of my preprint are wrong.
P.S. I should like to thank Paul Balmer who has given me the reference to
Schlichting's preprint.