  NGC 3311, the central galaxy of the Hydra I cluster, shows signatures of
recent infall of satellite galaxies from the cluster environment. Previous work
has shown that the line-of-sight velocity dispersion of the stars and globular
clusters in the extended halo of NGC 3311 rises up to the value of the cluster
velocity dispersion. We performed multi-object spectroscopic observations of
the diffuse stellar halo of NGC 3311 using VLT/FORS2 in MXU mode to mimic a
coarse `IFU'. We use pPXF to extract the kinematic information. We find a
homogeneous velocity and velocity dispersion field within r<10 kpc. Beyond this
radius, both the velocities and dispersions start to depend on azimuth angle
and show a significant intrinsic scatter. The inner spheroid of NGC 3311 can be
described as a slow rotator. Outside 10 kpc the cumulative angular momentum is
rising. If the radial dependence alone is considered, the velocity dispersion
does not simply rise but fills an increasingly large range of values with two
well defined envelopes. The lower envelope is about constant at 200 km/s. The
upper envelope rises smoothly, joining the velocity dispersion of the outer
cluster galaxies. We interpret this behaviour as the superposition of tracer
populations with increasingly shallower radial distributions between the
extremes of the inner stellar populations and the cluster galaxies. Simple
Jeans models illustrate that a range of of mass profiles with different
anisotropies can account for all observed velocity dispersions, including
radial MOND models. Jeans models using one tracer population with a unique
density profile are not able to explain the large range of the observed
kinematics. Previous claims about the cored dark halo of NGC 3311 are therefore
probably not valid. This may in general apply to central cluster galaxies with
rising velocity dispersion profiles, where infall processes are important.
