Can the broker execute the trade and become a counterparty instead of placing it on the exchange?

Can the broker in India, Trade against my position without placing the order on exchange? And can the broker do trades on my account? Without me knowing about it? I often get inaccurate P/L statements in ECN at End of the Day?

In India if one is trading on any recognized stock exchanges like NSE,BSE,MCX then any broker of those exchanges should place the trade on exchange itself instead the broker becoming the counter party. For every trade that happen on exchange there will be exchange order id which is unique for that particular trade that will be allocated by exchange, one can verify that unique id to know if the order is placed on to exchange or not.If you are not convinced with your broker explanation on pnl statements you can approach the concerned exchange.