We show that any sequence of integers satisfying necessary Dold’s congruences is realized as the se quence of fixed point indices of the iterates of an orientation-reversing homeomorphism of R^m for m ≥ 3. As an element of the construction of the above homeomorphism, we consider the class of boundary preserving homeomorphisms of R^m_+ and give the answer to the problem posed by Barge and Wójcik (2017) [2] providing a complete...