The phrase "acting on the orders" is correct and usable in written English.
It can be used when describing someone who is following or executing commands given by another person or authority.
Example: "The officer was acting on the orders of his superior when he made the arrest."
Alternatives: "following the orders" or "executing the commands".
Whether he was acting on the orders of others has not been raised.
The Indians were shot dead in Amritsar by riflemen acting on the orders of Brigadier General Reginald Dyer.
In retaliation, Czech agents, perhaps acting on the orders of Beneš's government in exile, bombed and shot Heydrich in May 1942 (he died in June).
Hamas leader Khaled Meshaal later said that members may have been behind the killings, but that they were not acting on the orders of group's political leadership.
Journalists reporting in rural areas frequently find their attempts to investigate stories blocked by thugs, apparently acting on the orders of local officials.
They were acting on the orders of the Iraqi Olympic Committee, which is in the hands of Iraq's Shia-dominated government.
The decision came after a state supervisory board, acting on the order of Abdullah Gul, the current president, issued a report in June voicing suspicions about the death.
Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another.
A4 Pakistan Tax Crackdown Beginning today, soldiers and revenue officers acting on orders from the eight-month-old military government will start delivering tax survey forms to businesses and homes in 13 cities to try to learn who owes how much and make them pay.
The duties are preemptive because the citizen must put aside the considerations she initially planned on acting on in order to treat the rest of her fellow citizens with proper respect.
They all claimed to be acting on the direct orders of officers loyal to Adolphe.
