  We point out unconventional mechanical properties of confined active fluids,
such as bacterial suspensions, under shear. Using a minimal model of an active
liquid crystal with no free parameters, we predict the existence of a window of
bacteria concentration for which a suspension of \textit{E.~Coli} effectively
behaves, at steady-state, as a negative viscosity fluid and reach quantitative
agreement with experimental measurements. Our theoretical analysis further
shows that a negative apparent viscosity is due to a non-monotonic local
velocity profile, and is associated with a non-monotonic stress vs. strain rate
flow curve. This implies that fixed stress and fixed strain rate ensembles are
not equivalent for active fluids.
