  We define twisted Hochschild homology for Green functors. This construction
is the algebraic analogue of the relative topological Hochschild homology
$THH_{C_n}(-)$, and it describes the $E_2$ term of the K\"unneth 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.
