Recently I've been requested to implement screen sharing in a CEF client whose purpose is peer to peer communication(Webrtc). I knew screen sharing was possible directly using getUserMedia in the past but they removed it and moved to extension API chrome.desktopCapture. After digging around Google, I've stumbled across a person who did implement screen sharing.
Here is the related issue https://bitbucket.org/chromiumembedded/cef/issues/1065/add-support-for-webrtc-based-screen
Related patch https://github.com/buglloc/cef-builds/blob/master/patches/allow_screen_sharing.patch
Since the guy who created the patch originally didnt post this here I wanted to get this known in case someone googles screen sharing and can't find anything.
I also made a blog post about step-by-step tutorial of how to apply the patch and recompile libcef,implement a screen picker for Windows(like in chrome extension) heavily using Win32 API. Here is the blog post link http://arkenthera.github.io/Enabling-CEF-to-Screen-Share-using-getUserMedia-API/