  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 have constructed
a new Breuil-Kisin module $\mathfrak{M}$ defined over the ring
$\mathfrak{S}:=W(\kappa)[[u]]$ and studied freeness and projectiveness
properties of such a module. Finally we have lifted the Breuil-Kisin module to
\'etale level following the $\mathscr{R}$-action and showed that if the
$p$-adic Tate module of a $p$-divisible group $\mathcal{G}$ over
$\mathscr{O}_K$ is free then the corresponding lifted Breuil-Kisin module is
free.
