The stable rank of some free product C*-algebras

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It is proved that the reduced group C*-algebra C*red(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G₁*G₂ where |G₁|>=2 and |G₂|>=3. This follows from a more general result where it is proved that if (A,tau) is the reduced free product of a family (Aᵢ,tauᵢ), i∈ I, of unital C*-algebras Aᵢ with normalized faithful traces tauᵢ, and if the family satisfies the Avitzour condition (i.e. the traces, tauᵢ, are not too lumpy in a specific sense), then A has stable rank one.