A special police force for Delhi whose reach into a State needs that State's consent
Background
The Central Bureau of Investigation draws its legal authority from The Delhi Special Police Establishment Act, 1946, which is Act 25 of 1946 and extends to the whole of India. Its forerunner was a police staff called the Special Police Establishment (War Department), set up by ordinance to look into bribery and corruption connected with departments of the Central Government. Under the Act the Central Government can set up a special police force, named the Delhi Special Police Establishment, to investigate in a Union Territory the offences notified for it. The Central Government specifies, by notification in the Official Gazette, which offences or classes of offences that force investigates. Superintendence of the force in matters under the Prevention of Corruption Act, 1988 vests in the Commission; in every other matter it vests in the Central Government. Administration of the force vests in an officer appointed by the Central Government and called the Director, who exercises such powers of an Inspector-General of Police as the Central Government specifies. The Director is appointed on the recommendation of a Committee. Words not defined in this Act carry the meaning given in the Central Vigilance Commission Act, 2003, and the force's powers reach a State only with that State's consent.
In plain words
DSPE Delhi Special Police Establishment — The special police force constituted under the 1946 Act, known today as the Central Bureau of Investigation.
General consent General consent — A standing permission a State gives for the central force to investigate within it, which a State can also withdraw.