  Given a semigroup of local homeomorphisms on a compact space X we consider
the corresponding semigroup of *-endomorphisms on C(X) and discuss the
possibility of extending it to an interaction group, a concept recently
introduced by the first named author. Under suitable hypotheses we may also
define a transformation groupoid whose C*-algebra turns out to be isomorphic to
the crossed product algebra for the interaction group. Several examples are
considered, including one which gives rise to a slightly different construction
and should be interpreted as being the C*-algebra of a certain polymorphism.

Operator Algebras;Dynamical Systems