drape

noun

hanging cloth used as a blind (especially for a window)

mantle
a sterile covering arranged over a patient's body during a medical examination or during surgery in order to reduce the possibility of contamination
the manner in which fabric hangs or falls
“They adjusted the drape of their garment.”

verb

arrange in a particular way
“drape a cloth”
place casually
“The cat draped herself on the sofa”
cover or dress loosely with cloth
“drape the statue with a sheet”
cover as if with clothing

cloak