Drop partition and rebuild global indexes "online"
Not in 11g.

Not even in 12c, but 12c makes life a bit easier, you can delay the "rebuild" part until a more appropriate time.

In 12c there is a new feature, called Asynchronous Global Index Maintenance. You can drop the partition, and that still leaves the global index usable, and marks the no longer needed index entries orphaned. Then later, you can clean up this index (DBMS_PART.CLEANUP_GIDX, or ALTER INDEX COALESCE CLEANUP, or the database can do it automatically for you as well (there is a pre-defined job for it called PMO_DEFERRED_GIDX_MAINT_JOB).