I'm using the symbol \otimes as a unary operator and it's vertical alignment doesn't seem right to me. It wants to sit a bit below the baseline. For example, if I define \newcommand{\myop}{\ensuremath \otimes}, then $\myop I$ becomes
and $F_{\myop I}$ becomes

I tried using \raisebox to fix this, e.g.,
\newcommand{\myop}{\ensuremath \raisebox{1pt}{$\otimes$}}
This fixes $\myop I$:

But \raisebox doesn't seem to be sensitive to subscripts. The operator stays the same size while everything around it shrinks:

The problem, I think, is that \raisebox creates its own LR box, which doesn't inherit the settings in the surrounding math environment. Is there a version of \raisebox that "respects math"?