  Spectropolarimetry is a powerful technique that has provided critical support
for the geometric unification model of local active galactic nuclei. In this
paper, we present optical (rest-frame UV) Keck spectropolarimetry of five
luminous obscured (Type 2) and extremely red quasars (ERQs) at z~2.5. Three
objects reach polarization fractions of >10% in the continuum. We propose a
model in which dust scattering is the dominant scattering and polarization
mechanism in our targets, though electron scattering cannot be completely
excluded. Emission lines are polarized at a lower level than is the continuum.
This suggests that the emission-line region exists on similar spatial scales as
the scattering region. In three objects we detect an intriguing 90 degree swing
in the polarization position angle as a function of line-of-sight velocity in
the emission lines of Ly-alpha, CIV and NV. We interpret this phenomenon in the
framework of a geometric model with an equatorial dusty scattering region in
which the material is outflowing at several thousand km/sec. Emission lines may
also be scattered by dust or resonantly. This model explains several salient
features of observations by scattering on scales of a few tens of pc. Our
observations provide a tantalizing view of the inner region geometry and
kinematics of high-redshift obscured and extremely red quasars. Our data and
modeling lend strong support for toroidal obscuration and powerful outflows on
the scales of the UV emission-line region, in addition to the larger scale
outflows inferred previously from the optical emission-line kinematics.
