  In this paper we present Multi Unit Spectroscopic Explorer (MUSE) integral
field unit spectroscopic observations of the $\sim70\times30$ kpc$^2$
Ly$\alpha$ halo around the radio galaxy 4C04.11 at $z = 4.5077$. High-redshift
radio galaxies (HzRGs) are hosted by some of the most massive galaxies known at
any redshift and are unique markers of concomitant powerful active galactic
nucleus (AGN) activity and star formation episodes. We map the emission and
kinematics of the Ly$\alpha$ across the halo as well as the kinematics and
column densities of eight HI absorbing systems at $-3500 < \Delta v < 0$ km
s$^{-1}$. We find that the strong absorber at $\Delta v \sim 0\,\rm km\,s^{-1}$
has a high areal coverage ($30\times30$ kpc$^2$), being detected across a large
extent of the Ly$\alpha$ halo, a significant column density gradient along the
southwest to northeast direction, and a velocity gradient along the radio jet
axis. We propose that the absorbing structure, which is also seen in CIV and NV
absorption, represents an outflowing metal-enriched shell driven by a previous
AGN or star formation episode within the galaxy and is now caught up by the
radio jet, leading to jet-gas interactions. These observations provide evidence
that feedback from AGN in some of the most massive galaxies in the early
Universe may play an important role in redistributing material and metals in
their environments.
