HK-good groupoid model conjecture for classifiable C*-algebras

A $C^*$-algebra is called classifiable if it belongs to the class of algebras classified by its Elliott invariant, and a groupoid model is HK-good when it has the homology–$K$-theory relationship desired in the HK conjecture. HK-good model conjecture. Any unital classifiable $C^*$-algebra admits an HK-good groupoid model. This would extend the groupoid approach to the classification program for unital classifiable $C^*$-algebras. The source presents this as an optimistic conjecture; it is not known whether the twist in the available twisted groupoid models can be removed, or whether an appropriate twisted variant of groupoid homology can be defined.