I defined a command \newcommand{\osum}[2]{\smashoperator[r]{\sum_{#1}}{#2}} with the intention to allow only the summand to be next to the sigma notation. However, this is not translated properly as shown by my MWE:
\documentclass{article}
\usepackage{mathtools}
\newcommand{\osum}[2]{\smashoperator[r]{\sum_{#1}} {#2}}
\newcommand{\orb}{\text{Orb}}
\begin{document}
[
O_G(X^\alpha) = \osum{X^\beta \in \orb_{G}(X^\alpha)}{X^\beta} = \osum{X^\beta \in \orb_G(\sigma^{-1}(X^\alpha))}{X^\beta} = \osum{X^\beta \in \orb_G(X^{\sigma(\alpha)})}{X^\beta} = O_G(X^{\sigma(\alpha)}).
]
\end{document}
This yields
I don't want the equal sign to hover over the subscript. I want it to respect the spacing of the osum object. Does anyone have any suggestions. Thanks.

