The Alpha Legion are one of the founding Legions of the Emperors Great Crusade, branded traitor during the Horus Heresy, by design they are the most obfuscated of the Traitor Legions. They fight wars through misdirection, suspicion, assassination and lies. Information is as much a tool for an Alpha Legionary as Bolter ammo.
When the Alpha Legion make their presence known on the Battlefield, it's likely a ruse to cover for a greater objective, or a double bluff. They also rely heavily on mortal operatives to carry out missions on their behalf and have infiltrated nearly every level of the Imperial bureaucracy, said to reach even into the Imperial Palace.
About the Army
My take on the Alpha Legion is one of Subtlety (for a Chaos Space Marine), where most Chaos Marines that fled into the Eye of Terror have spikes, tentacles and horns growing out of every plate, the Alpha Legion avoided this fate, fleeing to the Galactic east and so, my Legionaries rarely sport any Chaos Iconography, retaining much of their original Legion plate from the days of the Heresy or plate salvaged from Loyalist Space Marines that have fallen to the Blades of the Hydra. So I keep the corruption to a minimum.
It makes sense too, its difficult to imitate a Loyalist Space Marine chapter, or infiltrate a planetary government, with tentacles crawling out your face.
The Chaos portion of my Chaos Space Marine army is made up of the mortal elements from a Mechanicus Forge World. Starting with the lowliest cultists, the majority of which are factory workers, re-programmed servitors and general Imperial populous.
If I wish I can represent the world just on the verge of rebellion with a small handful of Legionaries puppeteering a hoard of cultists, all the way through to full chaos uprising, with Traitor Guardsmen of the blood pact, Daemon engines and even chaos knights.
The more advanced Corruption begins with the Mechanicus units, whos masters have dabbled with the powers of the dark gods turning them into mechanical daemon abominations. Kataphron destroyers infected with the Obliterator Virus, Daemon engines in the form of a Lord Discordant and Venom Crawlers, and a Chaos Knight.