  In general relativity, the fields on a black hole horizon are obtained from
those in the bulk by pullback and restriction. Similarly, in quantum gravity,
the quantized horizon degrees of freedom should result from restricting, or
pulling-back, the quantized bulk degrees of freedom. This is not yet fully
realized in the - otherwise very successful - quantization of isolated horizons
in loop quantum gravity. In this work we outline a setting in which the quantum
horizon degrees of freedom are simply components of the quantized bulk degrees
of freedom. There is no need to quantize them separately. We present evidence
that for a horizon of sphere topology, the resulting horizon theory is
remarkably similar to what has been found before.
