Invariants, torsion indices and oriented cohomology of complete flags

Annales scientifiques de l'École normale supérieure, vol. 46, fasc. 3, 2013, p. 405-448
(1^st online appearance of the preprint on the 8-5-2009)

We generalize the classical work of Demazure Invariants symétriques entiers des groupes de Weyl et torsion to arbitrary oriented cohomology theories and formal group laws. As an application, we provide a general algorithm to compute the ring structure of an oriented cohomology of a flag variety. Examples include Chow groups, Grothendieck groups, connective K-theory, algebraic cobordism of Levine and Morel, etc.