In this talk, we will talk about two seemingly unrelated actions, Promotion and Coxeter transformation. Promotion is defined purely combinatorially on the set of order ideals. By Rush and Shi, it is shown that this action has order 'h' for the order ideal poset of a cominuscule poset where h is the Coxeter number for the corresponding root system. On the other hand, the action of Auslander-Reiten translation on the level of Grothendieck group induces an action called the Coxeter transformation. We consider the action of the Coxeter transformation on the incidence algebra of the order ideal poset of a cominuscule poset. We prove that the Coxeter transformation is periodic on this algebra of order 'h+1' (up to a sign) in most cases. To understand the relationship between Promotion and Coxeter transformation, we will combinatorially describe the orbits of Auslander-Reiten translation on the order ideal posets of cominuscule posets.