The equivariant bordism formula for Nielsen numbers of iterates

Let $M$ be a connected closed manifold, let $f\colon M\to M$ be a self-map, and let $n\geq 2$. For the homotopy $n$-periodic point space, let $\ell_n^k(f)$ denote the relevant component of the invariant $\ell_n(f)$. Let $\pi_{\rho,k}$ be the set indexing the basis elements of $\mathbb Z[\pi_{\rho,k}]$, and let ${\mathcal N}_k(f)$ be the number of nonzero terms when $\ell_n^k(f)$ is expressed as a linear combination of those basis elements. The equivariant bordism formula. ${\mathcal N}_k(f)$ equals the Nielsen number of $f^k$. The statement gives a proposed numerical interpretation of the equivariant obstruction in terms of Nielsen theory; no resolution is supplied in the source.