The fixed-point algebra of tensor-product actions of finite Abelian groups on UHF-algebras

Let G be a finite Abelian group acting by tensor-product automorphisms on a UHF-C¹-algebra $\text{D}$. Extending a result of A. Kishimoto it is shown that the number of extremal traces on the fixed-point algebra $\text{D}$^G equals the cardinality of the subgroup K of automorphisms in G which are weakly inner in the trace representation of $\text{D}$.