Stark's Galois-equivariance conjecture for special values and regulators

Let $(\pi,V)$ be a representation of $G_{\mathbb{Q}}$ factoring through a finite Galois extension, and let $f$ be a fixed rational comparison isomorphism used to define Stark's regulator $R(\pi,f)$. For an automorphism $\alpha$ of $\mathbb{C}$, write $\pi^\alpha$ for the representation obtained using the embedding $\alpha\circ\iota_\infty$, and set

$$A(\pi^\alpha,f)=\frac{L^*((\pi^\alpha)^*,0)}{R(\pi^\alpha,f)}.$$

Stark's conjecture. For every automorphism $\alpha$ of $\mathbb{C}$,

$$A(\pi^\alpha,f)=A(\pi,f)^\alpha.$$

This asserts the expected Galois equivariance of the ratio of a leading Artin $L$-value to Stark's regulator. No resolution status is supplied in the text.