Equivariant K-Chevalley rules for Kac-Moody flag manifolds

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 $\lambda$-chain model of the first author and Postnikov. For Lakshmibai-Seshadri paths, our formulas are the Kac-Moody generalizations of results of Griffeth and Ram and Pittie and Ram for finite dimensional flag manifolds. A gap in the proofs of the mentioned results is addressed.