Isomorphism problem for Cayley combinatorial objects

A Cayley combinatorial object over a group $H$ is a relational structure on $H$ invariant under the group of right translations $H_R$. Cayley graphs over the group $H$ provide a well-known example of such objects. An isomorphism problem for Cayley graphs will be the central topic of my talk. I shall present Klin-Poeschel approach to this problem based on the method of Schur. In addition, some recent results about isomorphism problem for non-graphical Cayley objects will be discussed. (This talk will be part of Yom iuyn on Algebraic Combinatorics on on the occasion of the retirement of Prof. Mikhail Klin)