  We analyze the behavior of a suspension of active polar particles under
shear. In the absence of external forces, orientationally ordered active
particles are known to exhibit a transition to a state of non-uniform
polarization and spontaneous flow. Such a transition results from the interplay
between elastic stresses, due to the liquid crystallinity of the suspension,
and internal active stresses. In the presence of an external shear we find an
extremely rich variety of phenomena, including an effective reduction
(increase) in the apparent viscosity depending on the nature of the active
stresses and the flow-alignment property of the particles, as well as more
exotic behaviors such as a non-monotonic stress/strain-rate relation and yield
stress for large activities.
