I would recommend that you answer the question yourself, mostly because it would otherwise go on the Unanswered Questions queue for a silly reason. But also, answers from MathOverflow are not always appropriate for the audience of MathSE. Writing up a version of the answer there that is adapted to the MathSE audience does add value to this site. So adding examples and specific results would be a fine idea. And then since that thorough answer exists on MathOverflow, you don't need to write up a full answer here, but a synopsis with a link would be fine too. So maybe start your answer with something like
I've cross-posted this question to MathOverflow. Here is a summary of the answer given there. ...
And then while you did have to work to adapt your answer, if you still feel uncomfortable gaining some reputation based on the work of the answerer on MathOverflow, then you could mark your answer as community wiki (although I think some users would argue that't not intended use of community wiki).