I'd seen this block before and remembered it was called Crossroads so I tracked down some more info. The full name is Crossroads to Bachelor's Hall.
The pattern was first printed in 1906 in a Clara Stone booklet made available by
www.antiquepatternlibrary.org Here is the pdf link. You'll see that on the cover of the booklet is a swastika quilt. Look for quilt #31.
http://www.antiquepatternlibrary.org...ltPatterns.pdf
Recent article:
http://quiltingpiecebypiece.wordpres...ewold-pattern/
Detailed article on use of swastika in quilts.
http://www.quiltersmuse.com/Swastika...he-Design.html
You'd need an expert in dating fabrics to determine more closely when it was made. I think it looks 1920s. Do you know what year you're great-grandmother was born?