  In this paper we study the T-equivariant generalized cohomology of flag
varieties using two models, the Borel model and the moment graph model. We
study the differences between the Schubert classes and the Bott-Samelson
classes. After setup of the general framework we compute, for classes of
Schubert varieties of complex dimension <4 in rank 2 (including A_2, B_2, G_2
and A_1^{(1)}), moment graph representatives, Pieri-Chevalley formulas and
products of Schubert classes. These computations generalize the computations in
equivariant K-theory for rank 2 cases which are given in Griffeth-Ram
arXiv:math/0405333.
