  In this paper, by assuming a faithful action of a finite flat
$\mathbb{Z}_p$-algebra $\mathscr{R}$ on a $p$-divisible group $\mathcal{G}$
defined over the ring of $p$-adic integers $\mathscr{O}_K$, we construct a
category of new Breuil-Kisin module $\mathfrak{M}$ defined over the ring
$\mathfrak{S}:=W(\kappa)[\![u]\!]$ and study the freeness and projectiveness
properties of such a module.
