Prince Philip, who is the regiment's colonel-in-chief, presented it with a new ceremonial flag.
Since 2011, he had been a recruiter at the regiment's headquarters in the Tower of London.
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Two soldiers attached to the regiment were killed during the deployment in Helmand province.
The regiment said it was "devastated at the loss of this bright young soldier".
The regiment will replace the 1st Argyll and Sutherland Highlanders when their tour ends in July.
In our last battle, the regiment was attached to the 92nd Division -- all African-American.
The regiment has been based at Brawdy since 1996 and has the freedom of St Davids.
Since the formation of the Royal Regiment of Scotland in 2006, the regiment became a battalion.
In his role as the regiment's Colonel-in-Chief, he presented them with a campaign medal at the parade.
Prince William, who is colonel of the Irish Guards, wore the regiment's red tunic during the ceremony.
Princess Anne said it was "a privilege and a pleasure" to be presenting medals to the regiment.
Lisburn Mayor Paul Porter said the regiment has served all over the world with gallantry and bravery.
The memorial will serve as a permanent reminder of the sacrifices of all who served in the regiment.
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The regiment has served recently with the United Nations in Cyprus, and also in Bosnia and in Kosovo.
They are understood to be the last Falkland veterans serving in the regiment.
The SDLP said the decision send the regiment to Northern Ireland "raises the issue of who is in control".
Martin appealed to the regiment's sergeant major, who made inquiries on his behalf.
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My wife wrote to everyone she could think of including the Queen Mother who was the Colonel-in-Chief of the regiment.
Irish wolfhound Domhnall, who was carrying out his first public engagement as the regiment's mascot, was given the last sprig.
The regiment was created in 2007 through the merger of three single battalion regiments and the creation of a reserve one.
The Rangers were training on the West Coast facility, nearly 3, 000 miles from the regiment's home base in Fort Benning, Georgia.
By the time I was a senior the Regiment had become a bizarre parody of a military struggling with an unpopular war.
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There was confidential correspondence from Prime Minister Winston Churchill on the future of the regiment and the order assigning it regimental status.
His family and friends were among the thousands who turned out to celebrate the regiment being granted the freedom of the borough.
The regiment returned from a seven-month tour of Helmand Province last April.
The regiment was formed in 2007, but can trace its history back more than 200 years to the peninsular war against Napoleon's forces.
Of course, I might as well have had a stamp on my forehead saying "SAS, " such was the watch's popularity within the regiment.
The honour, agreed unanimously by the county's councillors, allows the regiment to march with "colours flying, drums beating and bayonets fixed" on ceremonial occasions.
The regiment was formed on St David's Day 2006 from The Royal Welch Fusiliers, The Royal Regiment of Wales and the Royal Welsh Regiment.
As part of the ceremony, soldiers from the regiment also attended a service at Ripon Cathedral to remember the two soldiers who died in Afghanistan.
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