The Abel Summation Method and Infinite Euler Characteristic

We develop a finiteness notion for unbounded chain complexes over a commutative noetherian integral domain $R$ employing the Abel summation method.

The algebraic K-theory of such complexes is defined, and shown to be non-trivial.

We also exhibit a natural map from the (usual) algebraic K-theory of $R$ into the new K-theory and show that its image contains a canonical infinite cyclic subgroup.