Abstract. In the present paper, we generalize the coproduct structure on nil Hecke rings introduced and studied by Kostant and Kumar to the context of an arbitrary algebraic oriented cohomology theory and its associated formal group law. We then construct an algebraic model of the T -equivariant oriented cohomology of the variety of complete flags.

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Contents 1. Introduction 1 2. Formal Demazure and push-pull operators 4 3. Two bases of the formal twisted group algebra 7 4. The Weyl and the Hecke actions 9 5. Push-pull operators and elements 11 6. The push-pull operators on the dual 13 7. Relations between bases coefficients 15 8. Another basis of the W Ξ -invariant subring 17 9. The formal Demazure algebra and the Hecke algebra 18 10. The algebraic restriction to the fixed locus on G/B 20 11. The algebraic restriction to the fixed locus on G/P 24 12. The push-pull operators on D ⋆ F 27 13. An involution 28 14. The non-degenerate pairing on the W Ξ -invariant subring 29 15. Push-forwards and pairings on D ⋆ F,Ξ 32 References 34

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