Equivariant evaluation on free loop spaces

There is a natural evaluation map on the free loop space which sends a loop to its values at the kth roots of unity. This map is equivariant with respect to the action of the cyclic group on k elements . We study the induced map in -equivariant cohomology with mod two coefficients in the cases where for . Received: 17 February 2000; in final form: 28 February 2001 / Published online: 18 January 2002