On the Drinfeld moduli problem of p-divisible groups

Let $O_D$ be the ring of integers in a division algebra of invariant $1/n$ over a p-adic local field. Drinfeld proved that the moduli problem of special formal $O_D$-modules is representable by Deligne's formal scheme version of the Drinfeld p-adic halfspace. In this paper we exhibit other moduli spaces of formal $p$-divisible groups which are represented by $p$-adic formal schemes whose generic fibers are isomorphic to the Drinfeld p-adic halfspace. We also prove an analogue concerning the Lubin-Tate moduli space.