On the KO –groups of toric manifolds

We consider the real topological K –groups of a toric manifold M, which turns out to be closely related to the topology of the small cover M_R, the fixed points under the canonical conjugation on M. Following the work of Bahri and Bendersky (2000), we give an explicit formula for the KO –groups of toric manifolds, and then we characterize the two extreme classes of toric manifolds according to their mod 2 cohomology groups as A.1/–modules.