K-Theory and Algebraic Groups

Abstract

The present paper is devoted to the description of certain interactions between the algebraic K-theory and the theory of algebraic groups. It consists of two parts. In the first part we consider an application of the algebraic K-theory to the rationality problem for algebraic groups. In the second part, conversely, we show how the theory of algebraic groups allows to compute K-groups of algebraic varieties with relatively large automorphism group.