Permutation-equivariant quantum K-theory I. Definitions. Elementary K-theory of $\overline M_{0,n}/S_n$

K-theoretic Gromov–Witten (GW) invariants of a compact Kähler manifold $X$ are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of $n$-pointed holomorphic curves in $X$. In this paper, we introduce K-theoretic GW-invariants cognizant of the $S_n$-module structure on the sheaf cohomology, induced by renumbering of the marked points, and compute some of these invariants for $X=\mathrm{pt}$.