  Galactic bars, made up of elongated and aligned stellar orbits, can lose
angular momentum via resonant torques with dark matter particles in the halo
and slow down. Here we show that if a stellar bar is decelerated to zero
rotation speed, it can flip the sign of its angular momentum and reverse
rotation direction. We demonstrate this in a collisionless N-body simulation of
a galaxy in a live counter-rotating halo. Reversal begins at small radii and
propagates outward. The flip generates a kinematically-decoupled core both in
the visible galaxy and in the dark matter halo, and counter-rotation generates
a large-scale warp of the outer disk with respect to the bar.
