Ring stacks conjecturally related to the stacks $BT_n^{G,\mu}$

Using the ring space of sheared Witt vectors, we define certain ring stacks. We suggest several models for the ring stacks.
Motivation: there is a conjectural description of the stack of n-truncated Barsotti-Tate groups and its Shimurian analogs in terms of the new ring stacks.