Let F and K be algebraically closed fields of characteristics p > 0 and 0, respectively. For any finite group G we denote by KRF(G) = K circle times(Z) G(0) (FG) the modular representation algebra of G over K where G(0)(FG) is the Grothendieck group of finitely generated FG-modules with respect to exact sequences. The usual operations induction, inflation, restriction, and transport of structure with a group isomorphism between the finitely generated modules of group algebras over F induce maps between modular representation algebras making KRF an inflation functor. We show that the composition factors of KRF are precisely the simple inflation functors S-C,V(i) where C ranges over all nonisomorphic cyclic p'-groups and V ranges over all nonisomorphic simple KOut(C)-modules. Moreover each composition factor has multiplicity 1. We also give a filtration of KRF. (c) 2007 Elsevier Inc. All rights reserved.