How to convert UTF8 combined Characters into single UTF8 characters in ruby?
Generally, you use Unicode Normalization to do this.
Using UnicodeUtils.nfkc using the gem unicode_utils (https://github.com/lang/unicode_utils) should get you the specific behavior you're asking for; unicode normalization form kC will use a compatibility decomposition followed by converting the string to a composed form, if available (basically what you asked for by your example). (You may also get close to what you want with normalization form c, sometimes acronymized NFC).
How to replace the Unicode gem on Ruby 1.9? has additional details.
In Ruby 1.8.7, you'd need do gem install Unicode, for which there is a similar function available.
Edited to add: The main reason why you'll probably want normalization form kC instead of just normalization form C is that ligatures (characters that are squeezed together for historical/typographical reasons) will first be decomposed to the individual characters, which is sometimes desirable if you're doing lexicographic ordering or searching).
These conversions don't always exist. The combination of U+0063 (c) with U+030C (combining caron) can be represented as a single character, for instance, but there's no precomposed character representing a lowercase 'w' with a caron (w̌).
Nevertheless, there exist libraries which can perform this composition where possible. Look for a Unicode function called "NFC" (Normalization Form: Composition). See, for instance: http://unicode-utils.rubyforge.org/classes/UnicodeUtils.html#M000015