How can I install a GFCI receptacle to provide protection to other devices?
Yes, look carefully at a GFI (or equivalently GFCI) outlet:



You can see the terminals at the top are labeled Line which means, upstream power.  The pair of terminals at the bottom are labeled Load, which means this is where to connect outlets downstream which are protected by this GFI.

Be careful not to bridge the line terminals to the load terminals!  A pigtail should only connect to the load terminals.