We generalize the approach of Adams by obtaining a character fornula relating the irreducible characters of $PGL(n)$ with those of certain covers of $SL(n)$. We then study the lifting of functions between covers of $SL(n)$ and $PGL(n)$. We use orbital integrals to obtain a formula for the lifting of characters as a dual to the formula relating the characters. This is based on the approach of Kazhdan and Flicker.