Have you tried syncing your reader? This usually will get books you checked out via your computer to appear on the reader.
However, the Kobo system is dependent on the same exact edition of the book being available on Overdrive and in the Kobo store. I've run into a few books where syncing wouldn't get the book onto my Kobo. In those cases, I had use Adobe Digital Editions to copy the book from my PC to my Kobo via USB.
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