The KO∗-rings of BTm, the Davis–Januszkiewicz spaces and certain toric manifolds

Abstract This paper contains an explicit computation of the K O ∗ -ring structure of an m -fold product of C P ∞ , the Davis–Januszkiewicz spaces and of toric manifolds which have trivial Sq 2 -homology. A key ingredient is the stable splitting of the Davis–Januszkiewicz spaces given by Bahri et al. (2009, 2010) [6] , [7] .