Infinite Loop Spaces Associated to Affine Kac-Moody Groups

The main purpose of this paper is to construct infinite loop spaces from affine Kac-Moody groups, It is well known that to each infinite class of classical groups over a commutative ring R , we can associate an infinite loop space G(R) by Quillen's plus construction.In this paper we generalize this fact to the cases of affine Kac-Moody groups.Roughly speaking, for each commutative ring R there are seven infinite classes of affine Kac-Moody groups over R , and to each infinite class we can associate an analogous infinite loop space.