  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.
