  The transport of slightly deformable chiral objects in a uniform shear flow
is investigated. Depending on the equilibrium configuration one finds up to
four different asymptotic states that can be distinguished by a lateral drift
velocity of their center of mass, a rotational motion about the center of mass
and deformations of the object. These deformations influence the magnitudes of
the principal axes of the second moment tensor of the considered object and
also modify a scalar index characterizing its chirality. Moreover, the
deformations induced by the shear flow are essential for the phenomenon of
dynamical symmetry breaking: Objects that are achiral under equilibrium
conditions may dynamically acquire chirality and consequently experience a
drift in the lateral direction.
