  Within the framework of metric-affine gravity (MAG, metric and an independent
linear connection constitute spacetime), we find, for a specific gravitational
Lagrangian and by using {\it prolongation} techniques, a stationary axially
symmetric exact solution of the vacuum field equations. This black hole
solution embodies a Kerr-deSitter metric and the post-Riemannian structures of
torsion and nonmetricity. The solution is characterized by mass, angular
momentum, and shear charge, the latter of which is a measure for violating
Lorentz invariance.
