The Witt vectors for Green functors

We define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology THHCn(−), and under flatness conditions it describes the E2 term of the Künneth spectral sequence for relative THH. Applied to ordinary rings, we obtain new algebraic invariants. Extending Hesselholt's construction of the Witt vectors of noncommutative rings, we interpret our construction as providing Witt vectors for Green functors.