We study $p$-divisible groups $G$ endowed with an action of the ring of
integers of a finite (possibly ramified) extension of $\mathbb{Q}_p$ over a
scheme of characteristic $p$. We suppose moreover that the $p$-divisible group
$G$ satisfies the Pappas-Rapoport condition for a certain datum $\mu$ ; this
condition consists in a filtration on the sheaf of differentials $\omega_G$
satisfying certain properties. Over a perfect field, we define the Hodge and
Newton polygons for such $p$-divisible groups, normalized with the action. We
show that the Newton polygon lies above the Hodge polygon, itself lying above a
certain polygon depending on the datum $\mu$. We then construct Hasse
invariants for such $p$-divisible groups over an arbitrary base scheme of
characteristic $p$. We prove that the total Hasse invariant is non-zero if and
only if the $p$-divisible group is $\mu$-ordinary, i.e. if its Newton polygon
is minimal. Finally, we study the properties of $\mu$-ordinary $p$-divisible
groups. The construction of the Hasse invariants can in particular be applied
to special fibers of PEL Shimura varieties models as constructed by Pappas and
Rapoport.