Negative regulator in the hedgehog/smoothened signaling pathway that acts by sequestering the GLI (GI1, GLI2 and GLI3) transcription factors in the cytoplasm (PubMed:10559945, PubMed:10564661, PubMed:10806483, PubMed:12068298, PubMed:12975309, PubMed:15367681, PubMed:22365972, PubMed:24217340, PubMed:24311597, PubMed:27234298, PubMed:28965847, PubMed:35831023). When smoothened signaling is initiated, GLI transcription factors dissociate from SUFU, translocate to the nucleus and activate expression of target genes (PubMed:24311597, PubMed:28965847, PubMed:35831023). In absence of smoothened signaling, the SUFU-GLI3 complex is recruited to cilia, leading to the efficient processing of full-length GLI3 into transcription repressor GLI3R: SUFU participates to GLI3 processing by promoting recruitment of GSK3B to GLI3 (PubMed:24311597, PubMed:28965847). May also act as a negative regulator of beta-catenin signaling (By similarity). Required for normal embryonic development (By similarity). Required for the proper formation of hair follicles and the control of epidermal differentiation (By similarity). {ECO:0000250|UniProtKB:Q9Z0P7, ECO:0000269|PubMed:10559945, ECO:0000269|PubMed:10564661, ECO:0000269|PubMed:10806483, ECO:0000269|PubMed:12068298, ECO:0000269|PubMed:12975309, ECO:0000269|PubMed:15367681, ECO:0000269|PubMed:22365972, ECO:0000269|PubMed:24217340, ECO:0000269|PubMed:24311597, ECO:0000269|PubMed:27234298, ECO:0000269|PubMed:28965847, ECO:0000269|PubMed:35831023}. This is the function of ENSG00000107882 (SUFU, SUFU negative regulator of hedgehog signaling).