Transcriptional regulator involved in different processes such as glucose metabolism, aerobic glycolysis and autophagy (By similarity). Recognizes and binds the forkhead DNA sequence motif (5'-GTAAACA-3') and can both act as a transcription activator or repressor, depending on the context (PubMed:22083952, PubMed:25451922). Together with FOXK1, acts as a key regulator of metabolic reprogramming towards aerobic glycolysis, a process in which glucose is converted to lactate in the presence of oxygen (By similarity). Acts by promoting expression of enzymes for glycolysis (such as hexokinase-2 (HK2), phosphofructokinase, pyruvate kinase (PKLR) and lactate dehydrogenase), while suppressing further oxidation of pyruvate in the mitochondria by up-regulating pyruvate dehydrogenase kinases PDK1 and PDK4 (By similarity). Probably plays a role in gluconeogenesis during overnight fasting, when lactate from white adipose tissue and muscle is the main substrate (By similarity). Together with FOXK1, acts as a negative regulator of autophagy in skeletal muscle: in response to starvation, enters the nucleus, binds the promoters of autophagy genes and represses their expression, preventing proteolysis of skeletal muscle proteins (By similarity). In addition to the 5'-GTAAACA-3' DNA motif, also binds the 5'-TGANTCA-3' palindromic DNA motif, and co-associates with JUN/AP-1 to activate transcription (PubMed:22083952). Also able to bind to a minimal DNA heteroduplex containing a G/T-mismatch with 5'-TRT[G/T]NB-3' sequence (PubMed:20097901). Binds to NFAT-like motifs (purine-rich) in the IL2 promoter (PubMed:1339390). Positively regulates WNT/beta-catenin signaling by translocating DVL proteins into the nucleus (PubMed:25805136). Also binds to HIV-1 long terminal repeat. May be involved in both positive and negative regulation of important viral and cellular promoter elements (PubMed:1909027). Component of SIN3A-, but not SIN3B-, containing multiprotein complexes (By similarity). Interacts with DVL1, DVL2 (when phosphorylated) and DVL3; the interaction induces DVL2 nuclear translocation (PubMed:25805136). Interacts with SUDS3 (PubMed:25805136). Interacts with BAP1 (when phosphorylated); leading to recruit the PR-DUB complex and repress FOXK2 target genes (PubMed:24748658, PubMed:25451922). Expressed in both lymphoid and non-lymphoid cells. The C-terminal part of the DNA-binding domain may contribute to DNA recognition specificity. Hyperphosphorylated during mitosis by CDK1 and, to a lower extent, CDK2 (PubMed:20810654). Phosphorylation at Ser-373 and Ser-428 affects stability by promoting degradation (PubMed:20810654). Was initially named FOXK1a by some reports (PubMed:12402362, PubMed:16624804). It should not be confused with FOXK1 (AC P85037) paralog. The N-terminal sequence differs due to frameshifts and sequencing errors. The N-terminal sequence differs due to frameshifts and sequencing errors. The N-terminal sequence differs due to frameshifts and sequencing errors.