On Normalizers of $C^{\ast }$-Subalgebras in the Cuntz Algebra ${\mathcal{O}}_n$. II

We investigate subalgebras $A$ of the Cuntz algebra ${\mathcal{O}}_n$ that arise as finite direct sums of corners of the UHF-subalgebra ${\mathcal{F}}_n$. For such an $A$, we completely determine its normalizer group inside ${\mathcal O}_n$.