Let G be an infinite countable group and A be a finite set.If Σ (U) AG is a strongly irreducible subshift of finite type,we endow a locally compact and Hausdorff topology on the homoclinic equivalence relation g on Σ and show that the reduced C*-algebra C*r (g) of g is a unital simple approximately finite (AF)-dimensional C*-algebra.The shift action of G on Σ induces a canonical automorphism action of G on the C*-algebra C*r (g).We give the notion of noncommutative dynamical entropy invariants for amenable group actions on C*-algebras,and show that,if G is an amenable group,then the noncommutative topological entropy of the canonical automorphism action of G on C*r (g) is equal to the topology entropy of the shift action of G on Σ.We also establish the variational principle with respect to the noncommutative measure entropy and the topological entropy for the C*-dynamical system (C*r (g),G).