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I use Times New Roman font for my report. But in the math expressions are not displayed Cyrillic characters.

Example:

\begin{equation}
  S_{ном.} = S_{123}
\end{equation}

output

\documentclass[a4paper, 14pt]{extreport} 

\usepackage[cm-default]{fontspec}
\setmainfont{Times New Roman}

\usepackage{titlesec}
\usepackage{indentfirst}
\usepackage{fncychap}
\usepackage{fancyhdr}
\usepackage[warn]{mathtext}

\usepackage[utf8]{inputenc}

\newfontfamily\cyrillicfont{Times New Roman}
\usepackage{polyglossia}
\setdefaultlanguage{russian}

\usepackage{amssymb,amsfonts,amsmath,mathtext,cite,enumerate,float, mathtext} 
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up vote 5 down vote accepted

You should use

\begin{equation}
  S_\textup{ном.} = S_{123}
\end{equation}

because that's text.

You can consider using unicode-math instead of mathtext

\usepackage{amsmath}
\usepackage{unicode-math}
\setmainfont{Times New Roman}
\setmathfont{XITS Math}

% \newfontfamily\cyrillicfont{Times New Roman}
\usepackage{polyglossia}
\setdefaultlanguage{russian}

but notice that amsmath must be loaded before it. This wouldn't change the way you input that subscript.

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