  We propose a state redistribution method for high order discontinuous
Galerkin methods on curvilinear embedded boundary grids. State redistribution
relaxes the overly restrictive CFL condition that results from arbitrarily
small cut cells and explicit time stepping. Thus, the scheme can take time
steps that are proportional to the size of cells in the background grid. The
discontinuous Galerkin scheme is stabilized by postprocessing the numerical
solution after each stage or step of an explicit time stepping method. This is
done by temporarily merging the small cells into larger, possibly overlapping
neighborhoods using a special weighted inner product. Then, the numerical
solution on the neighborhoods is returned to the base grid in a conservative
fashion. The advantage of this approach is that it uses only basic mesh
information that is already available in many cut cell codes and does not
require complex geometric manipulations. Finally, we present a number of test
problems that demonstrate the encouraging potential of this technique for
applications on curvilinear embedded geometries. Numerical experiments reveal
that our scheme converges with order $p+1$ in $L_1$ and between $p$ and $p+1$
in $L_\infty$ for problems with smooth solutions. We also demonstrate that
state redistribution is capable of capturing shocks.
