Selflessness for twisted group C*-algebras of amenable groups and their inclusions

For a discrete amenable group $G$ with a two-cocycle $σ$, we study when the twisted group $C^*$-algebra $C^*_r(G,σ)$ is selfless, in the sense of Robert. For a countably infinite abelian group $G$, this holds exactly when the commutator bicharacter of $σ$ is nondegenerate, that is, under Kleppner's