How do i use a cyrillic glyph/symbol/character in a math formula?

If you're not short of math symbol fonts, you can define a new one:

\documentclass{article}
\usepackage[X2,T1]{fontenc}

\DeclareSymbolFont{cyrillic}{X2}{cmr}{m}{n}
\SetSymbolFont{cyrillic}{bold}{X2}{cmr}{bx}{n}

\DeclareMathSymbol{\khk}{\mathord}{cyrillic}{139}

\begin{document}

$a+\khk(b)_{\khk(b)}$

\end{document}

The advantage of the X2 encoding is that it covers all (well, almost all) glyphs in the various Cyrillic encodings.

If you're short of symbol fonts, a less efficient solution is to use \text.

\documentclass{article}
\usepackage[X2,T1]{fontenc}
\usepackage{amsmath}

\DeclareRobustCommand{\khk}{%
  \mathord{\text{\usefont{X2}{cmr}{m}{n}\symbol{139}}}%
}

\begin{document}

$a+\khk(b)_{\khk(b)}$

\end{document}

You can change the type of the math atom, if it is not \mathord, into something else (\mathrel, if it should be a relation symbol).

You can also use directly the letter in the formulas, with UTF-8. This is for the second solution, the first one will work the same.

\documentclass{article}
\usepackage[X2,T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\DeclareUnicodeCharacter{04C3}{\khk}

\DeclareRobustCommand{\khk}{%
  \mathord{\text{\usefont{X2}{cmr}{m}{n}\symbol{139}}}%
}

\begin{document}

$a+Ӄ(b)_{Ӄ(b)}$

\end{document}

Sorry, no Japanese or Bengali, this way. Think to your readers who would have a hard time in deciphering those symbols.