  Let $G$ be an infinite group, $\kappa$ be an infinite cardinal, $\kappa\leq
\mid G\mid$ and let $\mathcal{E}_{\kappa}$ denotes a coarse structure on $G$
with the base $\{\{ (x,y): y\in F x F\}: F\in [G]^{<\kappa}\}$. We prove that
if either $\kappa< \mid G\mid$ or $\kappa= \mid G\mid$ and $\kappa$ is singular
then the Higson's corona $\nu _{\kappa} (G)$ of the coarse space $(G,
\mathcal{E}_{\kappa})$ is a singleton. If $\kappa= \mid G\mid$ and $\kappa$ is
regular then $\nu _{\kappa} (G)$ contains a copy of the space $U_{\kappa}$ of
$\kappa$-uniform ultrafilters on $\kappa$.
