  A nonstandard invariant fourth order operator acting on functions on a
manifold equipped with an almost Grassmannian structure with an arbitrary
trorsion is found by means of the curved translation principle. This operator
can be viewed as a Grassmannian analogue of the Paneitz operator well known
from conformal geometry. It is obtained by translating a Grassmannian analogue
of the Laplace operator to a certain tractor bundle with a specific tractor
connection, which is not normal in general.
