The algebraic/combinatorial method in the study of cohomology of flag varieties was started by Demazure and Bernstein-Gelfand-Gelfand in 1970s (for ordinary Chow groups), and were continued by Arabia, Kostant-Kumar, Bressler-Evens in 1980s-1990s (for equivariant singular cohomology, equivariant K-theory and complex cobordism). It was generalized to general oriented cohomology theory by Calmes-Petrov-Zainoulline, and later by myself with Calmes and Zainoulline.The dual of the algebra generated by divided difference operators will be the algebraic model of equivariant oriented cohomology of flag varieties, and many important structures(Bott-Samelson classes, push-pull maps, characteristic map) can be seen from this model. I will give main ideas of this construction. This construction is closely related with cohomology theory of Steinberg variety, which is the geometric model of Hecke algebra.