  We study a combined optimal control/stopping problem under a nonlinear
expectation ${\cal E}^f$ induced by a BSDE with jumps, in a Markovian
framework. The terminal reward function is only supposed to be Borelian. The
value function $u$ associated with this problem is generally irregular. We
first establish a {\em sub- (resp. super-) optimality principle of dynamic
programming} involving its {\em upper- (resp. lower-) semicontinuous envelope}
$u^*$ (resp. $u_*$). This result, called {\em weak} dynamic programming
principle (DPP), extends that obtained in \cite{BT} in the case of a classical
expectation to the case of an ${\cal E}^f$-expectation and Borelian terminal
reward function. Using this {\em weak} DPP, we then prove that $u^*$ (resp.
$u_*$) is a {\em viscosity sub- (resp. super-) solution} of a nonlinear
Hamilton-Jacobi-Bellman variational inequality.
