Considers a connected reductive $K$-group $H$ equipped with an action of a finite group $\Theta$ and studies the relationship between the buildings of $H$ and $G=(H^\Theta)^0$, under the assumption that the order of $\Theta$ is prime to the residue field characteristic $p$. It is shown that $\cB(G/K)$ can be identified with the set of fixed points $\cB(H/K)^\Theta$, and that the facets of $\cB(G/K)$ and the associated parahoric groups can be related to those for $H$. A special case of this set-up occurs when we take a connected reductive $K$-group $G$ and set $H=\tx{R}_{L/K}(G_L)$, where $L$ is a finite tamely ramified Galois extension of $K$. The results then relate Bruhat--Tits theory for $G/L$ and $G/K$. This is called \emph{tamely ramified descent}, and the resulting isomorphism $\cB(G/L)^{\tx{Gal}(L/K)}=\cB(G/K)$ was originally obtained in the thesis of Guy Rousseau by an entirely different method.