Prosecutors also accuse Gilroy of accessing Ms Pilley's email account between August 24 2009 and April 30 2010 and accessing her account on an internet dating website.
It is also alleged he repeatedly told police his relationship with Ms Pilley ended in December 2009 when the truth is that it continued and he wanted it to continue further.
It is alleged he visited Nike Air Max 90 Womens Neon
Lochgilphead High School in Argyll on May 5 when there was no requirement for him to do so and asked for bin bags which were given to him.
Gilroy, also from Edinburgh, denies the charges against him.
The murder charge alleges that Gilroy assaulted and injured Ms Pilley by unknown means in Thistle Street, or elsewhere, resulting in her death.
A further charge of attempting to defeat the ends of justice is broken into sub sections. They include claims that he bought air fresheners on May 4 2010 and repeatedly visited the basement and garage areas of the Infrastructure Management offices that same day when there was no need for him to do so.
David Gilroy in the dock accused of killing Air Max Classic 90
for legal reasons, and assaulting a man named Scott Stewardson in Edinburgh on November 9 2009.
He is accused of trying to cover up injuries on his hands with make up at Lothian and Borders Police headquarters and elsewhere.
He is also accused of threatening two children, who cannot be named Nike Air Max Black Woman
Gilroy faces other charges, including an allegation that he assaulted his wife Andrea on various occasions between January 1 2009 and May 18 2010.
They include allegations that he concealed Ms Pilley's body in the premises of Infrastructure Management in Thistle Street, in the Scottish capital, and transported it to various locations in Scotland in the boot of a car.
He is on trial before judge Lord Bracadale at the Air Max 90 Boots For Sale High Court in the city.
He is further accused of telling officers he saw Ms Pilley two days after he allegedly killed her.
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