How to make Polish letters capitalized at the beginning of each page in amsbook?

Question

I've been lately struggling with Polish letters in my thesis. Everything is fine in the text itself, but when I compile, the titles at the beginning of each page are displayed incorrectly. Let me show you what I mean.

"ś" and "ń" should be capitalized like the rest of the letters. "Pierścień Burnside'a" is a title of this chapter, of course. My thesis contain the following packages:

\usepackage[english, polish]{babel}
\usepackage{polski}
\usepackage[utf8]{inputenc}

Is this the blame of packages or is it something inside amsbook class? How can it be fixed? Thank you in advance for your help.

Here's an MWE -- please check out the header line on page 2.

\documentclass{amsbook}
%% (uncommenting the next four lines doesn't affect the header line)
%\usepackage[english, polish]{babel}
%\usepackage{polski}
%\usepackage[utf8]{inputenc}
%\usepackage[T1]{fontenc}
\usepackage{lipsum} % for filler text

\begin{document}
\chapter{Pierścień Burnside'a}
\lipsum[1-5] % generate slightly more than 1 page of filler text
\end{document}

Answer 1

Compiling the MWE under either XeLaTeX or LuaLaTeX succeeds in getting the capitalization of accented characters in the header line right.

\documentclass{amsbook}
\usepackage[english, polish]{babel}
\usepackage{lipsum}

\begin{document}
\chapter{Pierścień Burnside'a}
\lipsum[1-5]
\end{document}