  In this paper, we solve the existence problem of optimal stopping problem
under some kind of nonlinear expectation named g_\Gamma expectation which was
recently introduced in Peng, S.G. and Xu, M.Y. [8]. Our method based on our
preceding work on the continuous property of g_\Gamma solution. Generally, the
strict comparison theorem does not hold under such nonlinear expectations any
more, but we can still modify the classical method to find out an optimal
stopping time via continuous property. The mainly used theory in our paper is
the monotonic limit theorem of BSDE and nonlinear decomposition theorem of
Doob-Meyer's type developed by Peng S.G. [6]. With help of these useful
theories, a RCLL modification of the value process can also be obtained by a
new approach instead of down-crossing inequality.
