In gnu make: In a string, strip file paths from file names?

I have a string variable in my make file that is set to several file
names.  The names include the file paths, e.g., "../file.cpp ../../
file2.cpp ../DIR/file3.cpp".  In my make file, I need to convert that
to a string of just the file names, e.g., "file.cpp file2.cpp
file3.cpp".  Anyone know how to do that?  I looked at the gnu string
manipulation functions, but none seemed to be the answer.

Thanks!

Ken