  Let G be a smooth group scheme over $F_p$ equipped with a $G_m$-action such
that all weights of $G_m$ on the Lie algebra of G are not greater than 1. Let
$Disp_n^G$ be Eike Lau's stack of n-truncated G-displays (this is an algebraic
stack over $F_p$). In the case n=1 we introduce an algebraic stack equipped
with a morphism to $Disp_1^G$. We conjecture that if G=GL(d) then the new stack
is canonically isomorphic to the reduction modulo p of the stack of 1-truncated
Barsotti-Tate groups of height d and dimension d', where d' depends on the
action of $G_m$ on GL(d).
  We also discuss how to define an analog of the new stack for n>1 and how to
replace $F_p$ by $Z/p^n Z$.
