Suppose $V$ is a finite dimensional complex vector space and $f:V\to V$ is an automorphism. There is a natural extension $\Lambda^\bullet(f):\Lambda^\bullet(V)\to\Lambda^\bullet(V)$ to the exterior algebra $\Lambda^\bullet(V)$. If $f$ is of finite order, one can use the anti-commutative version of Molien's formula to compute the Hilbert series $f(t)$ of the fixed subalgebra $\Lambda^\bullet(V)^{\Lambda^\bullet(f)}$: if $G$ is the group generated by $f$, then $$f(t) = \frac{1}{|G|} \sum_{g\in G}\det(1+t g).$$
Is there a variation of this for $f$ not of finite order?
