Formule des traces et fonctorialité: Le début d'un programme

Author's comments:The most important point for the innocent or inexperienced reader of this paper to understand is that it is the stable trace formula that is here invoked. The stable trace formula, introduced many years ago in the reference [L2], developed and applied in the references [K1], [K2], [K3] and, more recently, in a very systematic way and to extremely good effect in [A2], is what allows the introduction of the Steinberg-Hitchin base and of the Poisson summation formula. I, myself, hope to develop some of the consequences of this, some certain, some as yet only possible, in subsequent papers. The present paper was written together with Edward Frenkel and Ngô Bảo Châu. The paper is expected to appear in Annales des sciences mathématiques du Québec.