An Explicit Cell Decomposition of the Wonderful Compactification of a Semisimple Algebraic Group We determine an explicit cell decomposition of the wonderful compactification of a semi\-simple algebraic group. To do this we first identify the $B\times B$-orbits using the generalized Bruhat decomposition of a reductive monoid. From there we show how each cell is made up from $B\times B$-orbits. Categories:14L30, 14M17, 20M17