有名な(yuumeina) famous, notorious
よく知られた(yoku shirareta) famous, well-known
左折(sasetsu) a left turn (of a car, bicycle, a person walking or jogging, etc.)
左旋回(hidari senkai) a left turn of an airplane

I think this is a physical left turn, and it probably refers to B's famous way of turning left. (i.e. some technique, skill, or method)
If it's in literature, there is some room for different ways how you translate the sentence, and here is my sample translation;
１）その時、B は有名な左折技術（の一つ）を披露した。Sono toki, B wa yuumeina sasetsu-gijutsu （no hitotsu）o hiroo shita.）It roughly translates as "when B showed one of his famous left-turn skills."　In Japanese, it's not always neccesary to say "one of...," so it's in parentheses.
２）その時 B が左折した。B の有名な左折方法の一つであった。Sono toki B ga sasetsu shita. B no yuumeina sasetsu houhou no hitotsu de atta. ....when B made a left turn. It was one of his famous left-turn methods.

Famous left turn means change opinion or direction of argument mid-sentance so to speak.

To change tack, try a different tack:
'to start using a different method for dealing with a situation, especially in the way that you communicate'
Example: "I've been very pleasant with them so far but if they don't cooperate, I may have to change tack." or "Instead of always asking him what he wants, why don't you try a different tack and tell him what you want?"

Or to change your tune:
'to change your opinion completely, especially because you know it will bring you an advantage.'
Example "He was against the idea to start with, but he soon changed his tune when I told him how much money he'd get out of it."

Some Alternatives:
一変 【いっぺん】 (n,vs) complete change; about-face;
翻す 【ひるがえす】 (v5s) to change (mind); to reverse (decision); to wave; to flutter;
心機一転 【しんきいってん】 (n) change of attitude;
心移り 【こころうつり】 (n) change of heart; fickleness;
変説 【へんせつ】 (n) change of opinion;
変わり身 【かわりみ】 (n) change of stance;
前説を翻す 【ぜんせつをひるがえす】 (exp) to change one's former opinion;
気が変わる 【きがかわる】 (v5) to change one's mind;
思い返す 【おもいかえす】 (v5s,vt) to re-think; to think back upon; to change one's mind;
翻意 【ほんい】 (n,vs) change one's mind;
思い直す 【おもいなおす】 (v5s,vt) to re-think; to think back upon; to change one's mind;
心変わり 【こころがわり】 (n) change one's mind; inconstancy; faithlessness;
観点を変える 【かんてんをかえる】 (exp) to change one's point of view;
百八十度 【ひゃくはちじゅうど】 180 degrees; complete change
豹変 【ひょうへん】 (n,vs) sudden change; complete change;
様変わり 【さまがわり】 (n) complete change;