In this talk, we present the recently defined unital algebra associated with a one-sided subshift over an arbitrary alphabet. For finite alphabets, the C*-algebraic version of this algebra coincides with the C*-algebra defined by Carlsen. We focus on infinite alphabets and show how conjugacy of two Ott-Tomforde-Willis subshifts is reflected as isomorphism of the associated algebras. This is joint work with Giuliano Boava, Gilles G. de Castro, and Daniel W. van Wyk.