Wikipedia
Cross-presentation is the ability of certain antigen-presenting cells to take up, process and present extracellular antigens with MHC class I molecules to CD8 T cells (cytotoxic T cells). Cross-priming, the result of this process, describes the naive cytotoxic CD8 T cell stimulation. This process is necessary for immunity against most tumors and against viruses that do not readily infect antigen-presenting cells, or impair dendritic cell normal function . It is also required for induction of cytotoxic immunity by vaccination with protein antigens, for example, tumour vaccination.
Cross-presentation is of particular importance, because it permits the presentation of exogenous antigens, which are normally presented by MHC II on the surface of infected dendritic cells to be also presented by MHC I without infecting the dendritic cell. Cross-presentation allows the dendritic cell to avoid using the endogenous proteasomal processing pathway, which otherwise would divert cellular resources away from MHC II presentation processes that present exogenous antigens after infection. Such a diversion could functionally impair the dendritic cell.