  Let $\Omega \subset {\bf R}^d$ be an open bounded set with Lipschitz boundary
$\Gamma$. Let $D_V$ be the Dirichlet-to-Neumann operator with respect to a
purely second-order symmetric divergence form operator with real Lipschitz
continuous coefficients and a positive potential $V$. We show that the
semigroup generated by $-D_V$ leaves $C(\Gamma)$ invariant and that the
restriction of this semigroup to $C(\Gamma)$ is a $C_0$-semigroup. We
investigate positivity and spectral properties of this semigroup. We also
present results where $V$ is allowed to be negative. Of independent interest is
a new criterium for semigroups to have a continuous kernel.
