I am looking for a method to compare and sort UTF-8 strings in C++ in a case-insensitive manner to use it in a custom collation function in SQLite.
What you really want is logically impossible. There is no locale-independent, case-insensitive way of sorting strings. The simple counter-example is "i" <> "I" ? The naive answer is no, but in Turkish these strings are unequal. "i" is uppercased to "İ" (U+130 Latin Capital I with dot above)
UTF-8 strings add extra complexity to the question. They're perfectly valid multi-byte char* strings, if you have an appropriate locale. But neither the C nor the C++ standard defines such a locale; check with your vendor (too many embedded vendors, sorry, no genearl answer here). So you HAVE to pick a locale whose multi-byte encoding is UTF-8, for the mbscmp function to work. This of course influences the sort order, which is locale dependent. And if you have NO locale in which const char* is UTF-8, you can't use this trick at all. (As I understand it, Microsoft's CRT suffers from this. Their multi-byte code only handles characters up to 2 bytes; UTF-8 needs 3)
wchar_t is not the standard solution either. It supposedly is so wide that you don't have to deal with multi-byte encodings, but your collation will still depend on locale (LC_COLLATE) . However, using wchar_t means you now choose locales that do not use UTF-8 for const char*.
With this done, you can basically write your own ordering by converting strings to lowercase and comparing them. It's not perfect. Do you expect L"ß" == L"ss" ? They're not even the same length. Yet, for a German you have to consider them equal. Can you live with that?