$K$-rings of smooth complete toric varieties and related spaces

Abstract

The $K$-rings of non-singular complex projective varieties as well as quasi-toric manifolds were described in terms of generators and relations in earlier work of the author with V. Uma. In this paper we obtain a similar description for the more general class of torus manifolds with locally standard torus action and orbit space a homology polytope, which includes the class of all smooth complete complex toric varieties.