  We present a consistent canonical formulation of the flat Oppenheimer-Snyder
model, including the Schwarzschild exterior. The switching between comoving and
stationary observer is realized by promoting the coordinate transformation
between dust proper time and Schwarzschild-Killing time to a canonical one.
This leads to two different forms of the Hamiltonian constraint, both (almost)
deparameterizable with regard to one of these times. A preliminary quantization
of these constraints reveals a consistent picture for both observers: the
singularity is avoided by a bounce.
