  Explicit combinatorial cancellation-free rules are given for the product of
an equivariant line bundle class with a Schubert class in the torus-equivariant
K-theory of a Kac-Moody flag manifold. The weight of the line bundle may be
dominant or antidominant, and the coefficients may be described either by
Lakshmibai-Seshadri paths or by the alcove model of the first author and
Postnikov. For Lakshmibai-Seshadri paths, our formulas are the Kac-Moody
generalizations of results of Griffeth-Ram and Pittie-Ram for finite
dimensional flag manifolds. A gap in the proofs of the mentioned results is
addressed.
