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.