  We prove a formula for the structure constants of multiplication of
equivariant Schubert classes in both equivariant cohomology and equivariant
K-theory of Kac-Moody flag manifolds G/B. We introduce new operators whose
coefficients compute these (in a manifestly polynomial, but not positive, way),
resulting in a formula much like and generalizing the positive
Andersen-Jantzen-Soergel/Billey and Graham/Willems formulae for the restriction
of classes to fixed points. Our proof involves Bott-Samelson manifolds, and in
particular, the (K-)cohomology basis dual to the (K-)homology basis consisting
of classes of sub-Bott-Samelson manifolds.
