Q:

scrlayer-scrpage - chapter on even pages, section on odd pages in scrreprt

I want to have a headings layout as in Anthony Knapp's Lie Groups, i.e. I want to have

the chapter on even, and the current section on odd pages.  I'm using the scrreprt class and tried using this solution:
\usepackage[
        automark,
        autooneside=false,
        headsepline,
    ]
    {scrlayer-scrpage}
        \clearpairofpagestyles
        \cfoot*{\pagemark}
        \chead{\headmark}
        \renewcommand\chaptermarkformat{\thechapter.\enskip}

but this only seems to work in the book class.  Also I want to have the page numbers on the bottom but I already go that myself. 

A:

You can use the internal command \Ifthispageodd and test if the page is even or odd, and then set the running heading as you like:

\documentclass{scrreprt}
\usepackage{blindtext}% only for dummy text

\usepackage[
  automark,
  autooneside=false,% <- if you want to use \leftmark and \rightmark in a one sided document
  headsepline=true
]{scrlayer-scrpage}
\pagestyle{scrheadings}
\cohead{\Ifthispageodd{\leftmark}{\rightmark}}
\cfoot*{\pagemark}

\begin{document}

\blinddocument
\end{document}

