  We construct a formal global quantization of the Poisson Sigma Model in the
BV-BFV formalism using the perturbative quantization of AKSZ theories on
manifolds with boundary and analyze the properties of the boundary BFV
operator. Moreover, we consider mixed boundary conditions and show that they
lead to quantum anomalies, i.e. to a failure of the (modified differential)
Quantum Master Equation. We show that it can be restored by adding boundary
terms to the action, at the price of introducing corner terms in the boundary
operator. We also show that the quantum GBFV operator on the total space of
states is a differential, i.e. squares to zero, which is necessary for a
well-defined BV cohomology.
