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We prove sign-alternation of the product structure constants in the basisdual to the basis consisting of the structure sheaves of Schubert varieties inthe torus-equivariant Grothendieck group of coherent sheaves on the partialflag varieties $G/P$ associated to an arbitrary symmetrizable Kac-Moody group$G$, where $P$ is any parabolic subgroup of finite type. This extends theprevious work of Kumar from $G/B$ to $G/P$. When $G$ is of finite type, i.e.,it is a semisimple group, then it was proved by Anderson-Griffeth-Miller.

Positivity in $T$-Equivariant $K$-theory of partial flag varieties associated to Kac-Moody groups