The over 450-year old chhatris, which are elevated, dome-shaped pavilions, are dedicated to local gods and goddesses and were allegedly snitched from the Sultana village in Jaislamer in March during an exercise of the Army there, Army sources said.
After the incident was brought to Army's notice, the authorities are probing the matter.
"The matter is under investigation," Defence PRO in Jodhpur Colonel S D Goswami said.
According to the charges, the antique structures were located near a pond but could not be accessed by the villagers due to an ongoing Army exercise there.
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The Brigadier had allegedly hired two local masons, who were working for the Army, to have the umbrellas taken out and installed at his residence in Gurgaon.
The structures were transported to the officer's house in Gurgaon in military transport in two installments and workers from Jaisalmer were hired to instal them there.
The Army exercises in the vast desert area in Jaisalmer near the Pakistan border and during the time of war drills, local population is not allowed to venture in those areas.