Zhilstroy are based in Kharkiv, where the remains of the victims of Malaysia Airlines flight MH17 were taken last month before being flown to the Netherlands. The second largest city in Ukraine, it remains in government hands despite being located just to the north of the area where the airliner was shot down.
The Ukranians are second seeds in City's group, and get proceedings underway when they play Northern Irish champions Glentoran at Falkirk Stadium this afternoon at 2.30pm. That is followed by City playing Slovakian champions Nove Zamky at Airdrie's Excelsior Stadium at 7.45pm.
Hosting a Champions League qualifying group is just another challenge to be overcome by City's formidable management duo of Laura Montgomery and Carol Anne Stewart. All the Scottish champions' previous qualification attempts have been away from home, so while home advantage should help City's attempt to reach the last 32 for a fourth successive season, the club manager and chairperson have been working tirelessly behind the scenes to make it happen.
"When we go away to play Champions League qualifiers we budget to lose £15,000," Montgomery explained. "It potentially could be even more expensive to host a group, but we have done everything possible to break even through sponsorship and other help from our club partners. And we certainly wouldn't be breaking even if we were paying ourselves to do this.
"The six group games are being played at Airdrie, Falkirk, and Broadwood. We've had great co-operation from all three clubs, but Falkirk in particular have been very helpful. They have donated their stadium for free, which is outstanding - it's a magnificent gesture from them."
With standards accelerating in women's football, City are not guaranteed to reach the last 32 even with home advantage. Montgomery, in fact, reckons that the task facing her side in the next six days is the toughest yet in Champions League qualifying. "That might sound strange when we had FC Twente in Holland last year, but we've never been in a situation before where all the other three teams were so strong," she pointed out.
"At least playing at home the preparation is all in our own hands - which it hasn't always been when we've gone away for the qualifiers. We've played in extreme temperatures and the food sometimes hasn't been great for the girls. We are the top seeds and we've got a good team."
City start with what - on paper at least - should be their most straightforward game against the Slovakian champions, but as ever, coach Eddie Wolecki Black is taking nothing for granted.
"We are well aware that Nove Zamky are in their second European campaign and will be a better team for the experience," he said.
Entry at the Excelsior Stadium is on the gate and costs £5 for adults and £2 for children.