Abstract: A projective toric scheme is specified by combinatorial data, viz., a polytope with integral vertex coordinates. I will show how the geometry of the polytope leads to a simple splitting result in the algebraic K-theory of the scheme. In the special case of projective space (given by a standard simplex) this reduces to the well-known splitting of K(P^n) into n+1 copies of the K-theory of the ground ring. - The combinatorial approach is flexible enough to include the case of schemes defined over an arbitrary (possibly non-commutative) ring.