The main role of the is to increase the binding ability of RNA polymerase to the lac operon promoter region.

catabolite activator protein (CAP)

Explanation:

Catabolite activator protein (CAP) is a homodimeric transcriptional activator required for transcription initiation of catabolite-sensitive genes in Escherichia coli. CAP contains a ligand-binding domain at its N-terminus and a DNA-binding domain at its C-terminus. CAP activates transcription by binding at target DNA sites on promoter sequences, thereby enhancing the ability of the RNA polymerase to bind and initiate transcription. CAP binds cyclic AMP (cAMP) to increase CAP’s affinity to DNA and thus activates the transcription of genes for catabolism, such as the lactose (lac) operon genes (the lac operon is a set of genes that encode for enzymes taking part in lactose metabolism).