  In this work, 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 when explicit time steppers are used. Thus, the
scheme can take 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 coarsening, or merging, the
small cells into larger, possibly overlapping neighborhoods using a special
weighted inner product. Then, the numerical solution on the neighborhoods is
refined back onto 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. We prove that state redistribution is conservative and
$p$-exact. Finally, we solve 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 $L_\infty$.
