Assuming you are using proper encoding (UTF-8), the reading application must use a font with the glyphs available.
Adobe Digital Editions, at least its pre-1.8 versions, use a default font that cannot be changed, and that lacks many glyphs, Cyrillic letters are notoriously missing. You can embed a font with all the needed characters in your ebook to solve this. Other readers allow the user to change the text font, so this is not as big a problem.
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