  We extend (scheme-theoretic) Bruhat-Tits theory to quasi-reductive groups
i.e. with trivial split unipotent radical over discretely valued henselian
non-archimedean fields $K$, whose ring of integers is excellent and residue
field is perfect, building on Bruhat-Tits I et II and the classification of
pseudo-reductive groups by Conrad-Gabber-Prasad. The buildings had been
constructed previously by Solleveld in a different manner, but they ultimately
coincide with ours. We were motivated by the geometry of affine Grassmannians
and give some applications at the end (compare also with previously submitted
work arXiv:1912.11918).
