  In this paper, we study reflected backward stochastic differential equations
driven by rough paths (rough RBSDEs), which can be understood as a
probabilistic representation of nonlinear rough partial differential equations
(rough PDEs) or stochastic partial differential equations (SPDEs) with
obstacles. The well-posedness in the sense of \cite{DF} is proved via a variant
of Doss-Sussman transformation. Moreover, we show that our rough RBSDEs can be
approximated by a sequence of penalized BSDEs with rough drivers. As
applications, firstly we provide the equivalence between rough RBSDEs and the
obstacle problem of rough PDEs. Secondly, we show the solution of rough RBSDE
solves the corresponding optimal stopping problem.
