  We consider the problem of building non-invertible quantum symmetries (as
characterized by actions of unitary fusion categories) on noncommutative tori.
We introduce a general method to construct actions of fusion categories on
inductive limit C*-algberas using finite dimenionsal data, and then apply it to
obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative
2-tori, of the even part of the $E_{8}$ subfactor on a noncommutative 3-torus,
and of $\text{PSU}(2)_{15}$ on a noncommutative 4-torus.
