  We study a discretization technique for the parabolic fractional obstacle
problem in bounded domains. The fractional Laplacian is realized as the
Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a
semi-infinite cylinder, which recasts our problem as a quasi-stationary
elliptic variational inequality with a dynamic boundary condition. The rapid
decay of the solution suggests a truncation that is suitable for numerical
approximation. We discretize the truncation with a backward Euler scheme in
time and, for space, we use first-degree tensor product finite elements. We
present an error analysis based on different smoothness assumptions
