The modular representation theory of iwahori hecke algebras and this theorys connection to groups of lie type is an area of rapidly expanding interest it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of iwahori hecke algebras at roots of unity this book is a particularly valuable addition to current research in this field using the framework provided by the kazhdan lusztig theory of cells the authors develop an analogue of james 1970 characteristic free approach to the representation theory of iwahori hecke algebras in general . The representation theory of hecke algebras at roots of unity has been studied to some extent with connections to other topics found see geck and jacon 11 but has not been completely . Hecke algebras arise naturally in the representation theory of finite or p adic cheval ley groups as endomorphism algebras of certain induced representations see carter lusztig and the references there they may also be viewed as quotients of group. Representations of hecke algebras at roots of unity geck meinolf seminaire bourbaki volume 1997 98 exposes 835 849 asterisque no 252 1998 expose no 836 23 p