  Using Poincare duality, we formulate a formula of Lefschetz type which
computes the Lefschetz number of an endomorphism of a separable, nuclear
C*-algebra satisfying Poincare duality and the Kunneth theorem. (The Lefschetz
number of an endomorphism is the graded trace of the induced map on K-theory
tensored with the complex numbers, as in the classical case.) We then consider
endomorphisms of Cuntz-Krieger algebras O_A. An endomorphism has an invariant,
which is a permutation of an infinite set, and the contracting and expanding
behavior of this permutation describes the Lefschetz number of the
endomorphism. Using this description we derive a closed polynomial formula for
the Lefschetz number depending on the matrix A and the presentation of the
endomorphism.
