Technically the cells manufacture the spike protein and your body will develop neutralizing antibodies to the spike protein, the cells will also display the ant

Technically the cells manufacture the spike protein and your body will develop neutralizing antibodies to the spike protein, the cells will also display the antigen (spike protein) on the surface of the cells in an MHC-antigen complex. That'll trigger CD4+ and CD8+ T-cells to also go into action. Some of the cells will be transported to lymph nodes and the gut for processing by the immune system. CD8+ cells will learn to recognize the MHC-antigen on the surface of cells and kills the "infected" cells. Then next time around B-cells and T-cells are primed from all this target practice and its a lot easier, even if the neutralizing antibodies wane.