Sheared Witt vectors and Barsotti-Tate groups

I will discuss a conjectural description of the $p$-adic completion of the stack of Barsotti-Tate groups (a.k.a. $p$-divisible groups). The description is in the spirit of the classical Dieudonné theory, but the ring scheme of Witt vectors is replaced by a certain ring space, which is called the space of sheared Witt vectors. In some sense, the ring space and the conjectural description go back to the works of Thomas Zink.