  Let $F$ be a non--Archimedean locally compact field (${\rm car}(F)\geq 0$),
${\bf G}$ be a connected reductive group defined over $F$, $\theta$ be an
$F$--automorphism of ${\bf G}$, and $\omega$ be a character of ${\bf G}(F)$. We
fix a Haar measure $dg$ on ${\bf G}(F)$. For a smooth irreducible
$(\theta,\omega)$--stable complex representation $\pi$ of ${\bf G}(F)$, that is
such that $\pi\circ \theta\simeq \pi\otimes \omega$, the choice of an
isomorphism $A$ from $\pi\otimes \omega$ to $\pi\circ \theta$ defines a
distribution $\Theta_\pi^A$, called the \og ($A$--)twisted character of
$\pi$\fg: for a compactly supported locally constant function $f$ on ${\bf
G}(F)$, we put $\Theta_\pi^A(f)={\rm trace}(\pi(fdg)\circ A)$. In this paper,
we study these distributions $\Theta_\pi^A$, without any restrictive hypothesis
on $F$, ${\bf G}$ or $\theta$. We prove in particular that the restriction of
$\Theta_\pi^A$ on the open dense subset of ${\bf G}(F)$ formed of those
elements which are $\theta$--quasi--regular is given by a locally constant
function, and we describe how this function behaves with respect to parabolic
induction and Jacquet restriction. This leads us to take up again the Steinberg
theory of automorphisms of an algebraic group, from a rationnal point of view.
