The chiral bag model couples the axial vector current of the quarks at the bag boundary to a pionic field outside of the bag. In the most common formulation, the chiral bag model basically replaces the interior of the skyrmion with the bag of quarks. Very curiously, most physical properties of the nucleon become mostly insensitive to the bag radius. Prototypically, the baryon number of the chiral bag remains an integer, independent of bag radius: the exterior baryon number is identified with the topological winding number density of the Skyrme soliton, while the interior baryon number consists of the valence quarks (totaling to one) plus the spectral asymmetry of the quark eigenstates in the bag. The spectral asymmetry is just the vacuum expectation value summed over all of the quark eigenstates in the bag. Other values, such as the total mass and the axial coupling constant , are not precisely invariant like the baryon number, but are mostly insensitive to the bag radius, as long as the bag radius is kept below the nucleon diameter. Because the quarks are treated as free quarks inside the bag, the radius-independence in a sense validates the idea of asymptotic freedom.