  We study interacting features of $S_N$ Orbifold CFTs. Concentrating on
characters (associated with $S_N$ Orbifold primaries) we first formulate a
novel procedure for evaluating them through $GL(\infty)_+$ tracing. The result
is a polynomial formula which we show gives results equivalent to those found
by Bantay. From this we deduce a hierarchy of commuting Hamiltonians featuring
locality in the induced space, and nonlinear string-type interactions.
