Every simple higher dimensional noncommutative torus is an AT algebra

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We prove that every simple higher dimensional noncommutative torus is an AT algebra.

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The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ) (2006, unknown): “Primary 19K14, 46L35, 46L55, 46L80; Secondary”
Regularity properties in the classification program for separable amenable C*-algebras (2007, background): “Establishing finite decomposition rank requires the full force of the classification theorems: a consequence of both theorems is that the algebras they cover are all in fact simple unital AH algebras of bounded”
The tracial Rokhlin property for actions of finite groups on C*-algebras (2006, background): “If α is approximately inner, requiring ∑ g∈G eg = 1 forces [1A] ∈ K0(A) to be divisible by the order of G, and therefore rules out many C*-algebras of interest.”
Finite cyclic group actions with the tracial Rokhlin property (2006, methodology): “The tracial Rokhlin property for actions of finite groups on C*-algebras was introduced in [26] for the purpose of proving that every simple higher dimensional noncommutative torus is an AT algebra (done in [ 27 ]), and proving that certain crossed products of such algebras by finite cyclic groups a”