  We consider a class of discretionary stopping problems within the
$G$-framework. We first establish the well-definedness of the stopping problem
under the $G$-expectation, by showing the quasi-continuity of the stopped
process. We then prove a verification theorem for $G$-optimal stopping problem.
One corollary is a direct proof for the well-known fact that the $G$-optimal
stopping problem is the same as the classical optimal stopping problem with
appropriate parameters, when the payoff function is concave or convex.
