  K-theoretic Gromov-Witten invariants of a compact Kahler manifold $X$ are
defined as super-dimensions of sheaf cohomology of interesting bundles over
moduli spaces of n-pointed holomorphic curves in X. With this article, we begin
a series of publications on K-theoretic Gromov-Witten invariants, cognizant of
the $S_n$-module structure on the sheaf cohomology, induced by renumbering of
the marked points. In the opening paper, we introduce such invariants, explain
how the representation-theoretic information with varying $S_n$ is incorporated
into generating functions of Gromov-Witten theory, and compute one of them, the
small J-function for $X=pt$, by using Kapranov's description of Deligne-Mumford
spaces $\overline{\mathcal M}_{0,n}$.
