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:

and

I tried using \raisebox to fix this, e.g., \raisebox{1pt}{$\otimes$}:

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"?