Crossed products by Z of algebras arising from reduced free group C *‐algebras

Assume that Γ is a free group on n generators g 1 , g 2 , …, g n , where 2 ⩽ n < ∞. Let Γ′ + be the subset{ g i 1m 1  g i 2m 2  …   g i km k  ∊   Γ   |   k ,   m 1 ,   … ,   m k   ∊   N }   ∪   { e } , and let P + ′ be the projection onto the subspace l 2 (Γ + ′) of l 2 (Γ). Every character χ of Γ induces an automorphism on C *‐algebra C r * (Γ, P + ′) generated by the reduced group C *‐algebra C r * (Γ) and the projection P + ′. We study the classification of the C *‐algebra crossed productsC r * ( Γ ,   P ′ + )   ⋊   α χ   Z , where α χ is the automorphism associated to χ .