  We present sufficient conditions for the transience and the existence of
local times of a Feller process, and the ultracontractivity of the associated
Feller semigroup; these conditions are sharp for L\'{e}vy processes. The proof
uses a local symmetrization technique and a uniform upper bound for the
characteristic function of a Feller process. As a byproduct, we obtain for
stable-like processes (in the sense of R.\ Bass) on $\R^d$ with smooth variable
index $\alpha(x)\in(0,2)$ a transience criterion in terms of the exponent
$\alpha(x)$; if $d=1$ and $\inf_{x\in\R} \alpha(x)\in (1,2)$, then the
stable-like process has local times.
