  The problem of how space-time responds to gravitating quantum matter in full
quantum gravity has been one of the main questions that any program of
quantization of gravity should address. Here we analyze this issue by
considering the quantization of a collapsing null shell coupled to spherically
symmetric loop quantum gravity. We show that the constraint algebra of
canonical gravity is Abelian both classically and when quantized using loop
quantum gravity techniques. The Hamiltonian constraint is well defined and
suitable Dirac observables characterizing the problem were identified at the
quantum level. We can write the metric as a parameterized Dirac observable at
the quantum level and study the physics of the collapsing shell and black hole
formation. We show how the singularity inside the black hole is eliminated by
loop quantum gravity and how the shell can traverse it. The construction is
compatible with a scenario in which the shell tunnels into a baby universe
inside the black hole or one in which it could emerge through a white hole.
