  Using a nonlinear version of the tautological bundle over Gra{\ss}mannians,
we construct a transgression map for differential characters from $M$ to the
nonlinear Gra{\ss}mannians $\mathrm{Gr}^S(M)$ of submanifolds of $M$ of a fixed
type $S$. In particular, we obtain prequantum circle bundles of the nonlinear
Gra\ss{}mannian endowed with the Marsden-Weinstein symplectic form. The
associated Kostant-Souriau prequantum extension yields central Lie group
extensions of a group of volume-preserving diffeomorphisms integrating
Lichnerowicz cocycles.
