Equivariant K-theory of Bott towers. Application to the multiplicative structure of the equivariant K-theory offlag varieties

(Equivariant K-theory of Bott towers. Application to the multiplicative structure of the equivariant K-theory of flag varieties) We construct a basis of the equivariant K-theory of Bott towers, and we describe precisely the multiplicative structure of these algebras. We deduce similar results for Bott-Samelson varieties. Thanks to the link between flag varieties and Bott-Samelson varieties, we give a method to compute the structure constants of the equivariant K-theory of flag varieties in the basis constructed by Kostant and Kumar in [18].