$p$-local stable splitting of quasitoric manifolds

We show a homotopy decomposition of $p$-localized suspension $\mathrm{\Sigma }{M}_{(p)}$ of a quasitoric manifold $M$ by constructing power maps. As an application we investigate the $p$-localized suspension of the projection $\pi$ from the moment-angle complex onto $M$, from which we deduce its triviality for $p>\dim M/2$\mathrm{.}Wealsodiscussnon-trivialityof$\pi_{(p)}$and$\Sigma^\infty\pi$.