For diagonal AH-algebra A, A ⊗ B is K-stable for all B iff matrix block sizes grow unbounded; this applies to non-Z-stable Villadsen algebras and all simple unital infinite-dimensional diagonal AH-algebras.
The homotopy groups of the unitary groups of non-commutative tori
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Tensorial Permanence of $K$-Stability for Diagonal AH-Algebras
For diagonal AH-algebra A, A ⊗ B is K-stable for all B iff matrix block sizes grow unbounded; this applies to non-Z-stable Villadsen algebras and all simple unital infinite-dimensional diagonal AH-algebras.