  Let $X$ be a generic quasi-symmetric representation of a connected reductive
group $G$. The GIT quotient stack $\mathfrak{X}=[X^{\rm ss}(\ell)/G]$ with
respect to a generic $\ell$ is a (stacky) crepant resolution of the affine
quotient $X/G$, and it is derived equivalent to a noncommutative crepant
resolution (=NCCR) of $X/G$. Halpern-Leistner and Sam showed that the derived
category $\mathrm{D}^b(\mathrm{coh}~\mathfrak{X})$ is equivalent to certain
subcategories of $\mathrm{D}^b(\mathrm{coh}~[X/G])$, which are called magic
windows. This paper studies equivalences between magic windows that correspond
to wall-crossings in a hyperplane arrangement in terms of NCCRs. We show that
those equivalences coincide with derived equivalences between NCCRs induced by
tilting modules, and that those tilting modules are obtained by certain
operations of modules, which is called exchanges of modules. When $G$ is a
torus, it turns out that the exchanges are nothing but iterated Iyama--Wemyss
mutations. Although we mainly discuss resolutions of affine varieties, our
theorems also yield a result for projective Calabi-Yau varieties. Using
techniques from the theory of noncommutative matrix factorizations, we show
that Iyama--Wemyss mutations induce a group action of the fundamental group
$\pi_1(\mathbb{P}^1 \backslash\{0,1,\infty\})$ on the derived category of a
Calabi-Yau complete intersection in a weighted projective space.
