Running 'yum install *.rpm' on my Fedora system gives "Package libobasis3.5-base-3.5.3-2.i586.rpm is not signed" and the installation aborts

Installation from rpm fails on Fedora.

Try to use option --nogpgcheck. So your line will be like that:

yum install *.rpm --nogpgcheck

But are you sure about the use of *.rpm?

Good luck!