  It is well known that given a finitely generated torsion module $M$ over the
Iwasawa algebra $\mathbb Z_p[[\Gamma]]$, where $\Gamma \cong \mathbb Z_p$,
there exists a continuous $p$-adic character $\rho$ of $\Gamma$ such that, for
the twist $M(\rho)$ of $M$, the $\Gamma_n := \Gamma^{p^n}$ Euler
characteristic, i.e. $\chi(\Gamma_n, M(\rho))$, is finite for every $n$. We
prove a generalization of this result by considering modules over the Iwasawa
algebra of a general $p$-adic Lie group $G$, instead of $\Gamma$. We relate
this twisted Euler characteristic to the evaluation of the {\it Akashi series}
at the twist and in turn use it to indicate some application to the Iwasawa
theory of elliptic curves. This article is a natural generalization of the
result established in [JOZ].
