Let n be an integer greater than or equal to 2. An n-potent is an element e of a ring R such that e^n = e. In this paper, we study n-potents in matrices over R and use them to construct an abelian group K_0^n(R). If A is a complex algebra, there is a group isomorphism from K_0^n(A) to (K_0(A))^(n-1) for all n greater than or equal to 2. However, for algebras over cyclotomic fields, this is not true in general. We consider K_0^n as a covariant functor, and show that it is also functorial for a generalization of homomorphism called an n-homomorphism.