K-theory of torus manifolds

A torus manifold was introduced and first studied by Hattori and Masuda in [hm]. Recently in [mp], Masuda and Panov, among other results, describe the cohomology ring structure of a torus manifold. In this note we shall describe the topological K-ring of a class of torus manifolds (those for which the orbit space under the action of the compact torus is a homology polytope whose nerve is shellable) in terms of generators and relations. Since these torus manifolds include the class of quasi-toric manifolds this is a generalization of our earlier results ([su]).