Immunology: Processing and presenting of exogenous antigen by APC?

During the exogenous pathway, the APC ingests the antigen, digests it, combines it with MHC cl two and presents it on it membrane. The MHC is synthesized in the rough ER and is combined with and invariant chain. it then travels to the golgi and out into the cytoplasm. At which stage is the invariant chain digested leaving only the CLIP? is this whilst it is in the golgi or after it leaves? thanks