There are no native Linux ebook readers than offer sync capabilities, although Kobo might produce one. So Google is currently your only option under Linux, because it is the only one offering a web-based reading tool.
Amazon never lets a competitor get very far ahead, though, and it has announced
Kindle for the Web. This is currently only for selected ebook samples, but as the above link says
Quote:
Coming Soon to Kindle for the Web
* Read the full text of Kindle books in your web browser. No download or installation required.
* Synchronize your library, last page read, bookmarks, notes, and highlights with Kindle and Kindle-compatible devices including PC, Mac, iPhone, iPad, BlackBerry, and Android phones.
* Bookstores, authors, retailers, bloggers and other website owners will be able to offer Kindle books from their own sites, let their readers start enjoying the full text of these books instantly, and earn affiliate fees for doing so.
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The last point (affiliate fees) is Amazon's primary goal, but reading via the browser does advance the Kindle's reach significantly.
Like Google, this will likely require internet access while reading via "for web".