  A thin shell of light-like dust with its own gravitational field is studied
in the special case of spherical symmetry. The action functional for this
system due to Louko, Whiting, and Friedman is reduced to Kucha\v{r} form: the
new variables are embeddings, their conjugate momenta, and Dirac observables.
The concepts of background manifold and covariant gauge fixing, that underlie
these variables, are reformulated in a way that implies the uniqueness and
gauge invariance of the background manifold. The reduced dynamics describes
motion on this background manifold.
